Time Value of Money. Appendix


 Benjamin Cobb
 3 years ago
 Views:
Transcription
1 1 Appendix Time Value of Money After studying Appendix 1, you should be able to: 1 Explain how compound interest works. 2 Use future value and present value tables to apply compound interest to accounting transactions. BrooksElliott/iStockphoto Doug Norman Crystals/Alamy
2 Appendix 1 Time Value of Money 699 Time value of money is widely used in business to measure today s value of future cash outflows or inflows and the amount to which liabilities (or assets) will grow when compound interest accumulates. In transactions involving the borrowing and lending of money, the borrower usually pays interest. In effect, interest is the time value of money. The amount of interest paid is determined by the length of the loan and the interest rate. However, interest is not restricted to loans made to borrowers by banks. Investments (particularly, investments in debt securities and savings accounts), installment sales, and a variety of other contractual arrangements all include interest. In all cases, the arrangement between the two parties the note, security, or purchase agreement creates an asset in the accounting records of one party and a corresponding liability in the accounting records of the other. All such assets and liabilities increase as interest is earned by the asset holder and decrease as payments are made by the liability holder. COMPOUND INTEREST CALCULATIONS Compound interest is a method of calculating the time value of money in which interest is earned on the previous periods interest. That is, interest for the period is added to the account balance and interest is earned on this new balance in the next period. In computing compound interest, it s important to understand the difference between the interest period and the interest rate: The interest period is the time interval between interest calculations. The interest rate is the percentage that is multiplied by the beginningofperiod balance to yield the amount of interest for that period. The interest rate must agree with the interest period. For example, if the interest period is one month, then the interest rate used to calculate interest must be stated as a percentage per month. When an interest rate is stated in terms of a time period that differs from the interest period, the rate must be adjusted before interest can be calculated. For example, suppose that a bank advertises interest at a rate of 12% per year compounded monthly. Here, the interest period would be one month. Since there are 12 interest periods in one year, the interest rate for one month is onetwelfth the annual rate, or 1%. In other words, if the rate statement period differs from the interest period, the stated rate must be divided by the number of interest periods included in the rate statement period. A few examples of adjusted rates follow: OBJECTIVE 1 Explain how compound interest works. Stated Rate Adjusted Rate for Computations 12% per year compounded semiannually 6% per sixmonth period (12%/2) 12% per year compounded quarterly 3% per quarter (12%/4) 12% per year compounded monthly 1% per month (12%/12) If an interest rate is stated without reference to a rate statement period or an interest period, assume that the period is one year. For example, both 12% and 12% per year should be interpreted as 12% per year compounded annually. Compound interest means that interest is computed on the original amount plus undistributed interest earned in previous periods. The simplest compound interest calculation involves putting a single amount into an account and adding interest to it at the end of each period. CORNERSTONE A11 (p. 700) shows how to compute future values using compound interest.
3 700 Appendix 1 Time Value of Money CORNERSTONE A11 Computing Future Values Using Compound Interest Information: An investor deposits $20,000 in a savings account on January 1, The bank pays interest of 6% per year compounded monthly. Why: When deposits earn compound interest, interest is earned on the interest. Assuming that the only activity in the account is the deposit of interest at the end of each month, how much money will be in the account after the interest payment on March 31, 2015? Solution: Monthly interest will be ½% (6% per year/12 months). Account balance, 1/1/15 $20, January interest ($20, ½%) Account balance, 1/31/15 20, February interest ($20, ½%) Account balance, 2/28/15 20, March interest ($20, ½%) Account balance, 3/31/15 $20, Note: Here, interest was the only factor that altered the account balance after the initial deposit. In more complex situations, the account balance is changed by subsequent deposits and withdrawals as well as by interest. Withdrawals reduce the balance and, therefore, the amount of interest in subsequent periods. Additional deposits have the opposite effect, increasing the balance and the amount of interest earned. As you can see in Cornerstone A11, the balance in the account continues to grow each month by an increasing amount of interest. The amount of monthly interest increases because interest is compounded. In other words, interest is computed on accumulated interest as well as on principal. For example, February interest of $ consists of $100 interest on the $20,000 principal and 50 interest on the $100 January interest ($ ¼ 50 ). In Cornerstone A11, the compound interest only amounts to $1.50. That might seem relatively insignificant, but if the investment period is sufficiently long, the amount of compound interest grows large even at relatively small interest rates. For example, suppose your parents invested $1,000 at ½% per month when you were born with the objective of giving you a university graduation present at age 21. How much would that investment be worth after 21 years? The answer is $3,514. In 21 years, the compound interest is $2,514 more than 2½ times the original principal. Without compounding, interest over the same period would have been only $1,260. The amount to which an account will grow when interest is compounded is the future value of the account. Compound interest calculations can assume two fundamentally different forms: calculations of future values calculations of present values As shown, calculations of future values are projections of future balances based on past and future cash flows and interest payments. In contrast, calculations of present values are determinations of present amounts based on expected future cash flows.
4 PRESENT VALUE OF FUTURE CASH FLOWS Whenever a contract establishes a relationship between an initial amount borrowed or loaned and one or more future cash flows, the initial amount borrowed or loaned is the present value of those future cash flows. The present value can be interpreted in two ways: From the borrower s viewpoint, it is the liability that will be exactly paid by the future payments. From the lender s viewpoint, it is the receivable balance that will be exactly satisfied by the future receipts. For understanding cash flows, cash flow diagrams that display both the amounts and the times of the cash flows specified by a contract can be quite helpful. In these diagrams, a time line runs from left to right. Inflows are represented as arrows pointing upward and outflows as arrows pointing downward. For example, suppose that Hilliard Corporation borrows $100,000 from Citizens Bank of New Liskeard on January 1, The note requires three $38, payments, one each at the end of 2015, 2016, and 2017, and includes interest at 8% per year. The cash flows for Hilliard are shown in Exhibit A11. Appendix 1 Time Value of Money 701 Cash Flow Diagram Exhibit A11 $100,000 $38, $38, $38, /1/15 12/31/15 12/31/16 12/31/17 The calculation that follows shows, from the borrower s perspective, the relationship between the amount borrowed (the present value) and the future payments (future cash flows) required by Hilliard s note. Amount borrowed, 1/1/15 $100, Add: 2015 interest ($100, ) 8, Subtract payment on 12/31/15 (38,803.35) Liability at 12/31/15 69, Add: 2016 interest ($69, ) 5, Subtract payment on 12/31/16 (38,803.35) Liability at 12/31/16 35, Add: 2017 interest ($35, ) 2, Subtract payment on 12/31/17 (38,803.35) Liability at 12/31/17 $ 0.00 Present value calculations like this one are future value calculations in reverse. Here, the three payments of $38, exactly pay off the liability created by the note. Because the reversal of future value calculations can present a burdensome and sometimes difficult algebraic problem, shortcut methods using tables have been developed (see Exhibits A17, A18, A19, and A110, pp , discussed later in this appendix).
5 702 Appendix 1 Time Value of Money Interest and the Frequency of Compounding The number of interest periods into which a compound interest problem is divided can make a significant difference in the amount of compound interest. For example, assume that you are evaluating four 1year investments, each of which requires an initial $10,000 deposit. All four investments earn interest at a rate of 12% per year, but they have different compounding periods. The data in Exhibit A12 show the impact of compounding frequency on future value. Investment D, which offers monthly compounding, accumulates $68 more interest by the end of the year than investment A, which offers only annual compounding. Exhibit A12 Effect of Interest Periods on Compound Interest Investment Interest Period I N Calculation of Future Amount in One Year* A 1 year 12% 1 ($10, ) ¼$11,200 B 6 months 6% 2 ($10, ) ¼ 11,236 C 1 quarter 3% 4 ($10, ) ¼ 11,255 D 1 month 1% 12 ($10, ) ¼ 11,268 *The multipliers (1.12 for Investment A, for investment B, etc.) are taken from the future value table in Exhibit A17 (p. 717). Use future value and present value tables to apply compound interest to accounting transactions. FOUR BASIC COMPOUND INTEREST PROBLEMS Any present value or future value problems can be broken down into one or more of the following four basic problems: computing the future value of a single amount computing the present value of a single amount computing the future value of an annuity computing the present value of an annuity Computing the Future Value of a Single Amount In computing the future value of a single amount, the following elements are used: f: the cash flow FV: the future value n: the number of periods between the cash flow and the future value i: the interest rate per period To find the future value of a single amount, establish an account for f dollars and add compound interest at i percent to that account for n periods: FV ¼ (f )(1 þ i) n The balance of the account after n periods is the future value. Because people frequently need to compute the future value of a single amount, tables have been developed to make it easier. Therefore, instead of using the formula above, you could use the future value table in Exhibit A17 (p. 717), where M 1 is the multiple that corresponds to the appropriate values of n and i: FV ¼ (f )(M 1 ) For example, suppose Allied Financial loans $200,000 at a rate of 6% per year compounded annually to an auto dealership dealer for four years. Exhibit A13 shows how
6 Appendix 1 Time Value of Money 703 Future Value of a Single Amount: An Example Exhibit A13 to compute the future value (FV) at the end of the four years the amount that will be repaid. Assuming Allied s viewpoint (the lender s), using a compound interest calculation, the unknown future value (FV) would be found as follows: Amount loaned $200, First year s interest ($200, ) 12, Loan receivable at end of first year 212, Second year s interest ($212, ) 12, Loan receivable at end of second year 224, Third year s interest ($224, ) 13, Loan receivable at end of third year 238, Fourth year s interest ($238, ) 14, Loan receivable at end of the fourth year $252, As you can see, the amount of interest increases each year. This growth is the effect of computing interest for each year based on an amount that includes the interest earned in prior years. The shortcut calculation, using the future value table (Exhibit A17, p. 717), would be as follows: FV ¼ (f )(M 1 ) ¼ ($200,000)(1:26248) ¼ $252,496 You can find M 1 at the intersection of the 6% column (i ¼ 6%) and the fourth row (n ¼ 4) or by calculating This multiple is the future value of the single amount after having been borrowed (or invested) for four years at 6% interest. The future value of $200,000 is 200,000 times the multiple. Note that there is a difference between the answer ($252,495.39) developed in the compound interest calculation and the answer ($252,496) determined using the future value table. This is because the numbers in the table have been rounded to five decimal places. If they were taken to eight digits ( ¼ ), the two answers would be equal. CORNERSTONE A12 shows how to compute the future value of a single amount. CORNERSTONE A12 Computing Future Value of a Single Amount Information: Kitchener Company sells an unneeded factory site for $200,000 on July 1, Kitchener expects to purchase a different site in 18 months so that it can expand into a new market. Meanwhile, Kitchener decides to invest the $200,000 in a money market fund that is guaranteed to earn 6% per year compounded semiannually (3% per sixmonth period). (Continued)
7 704 Appendix 1 Time Value of Money Why: The future value of a single amount is the original cash flow plus compound interest as of a specific future date. 1. Draw a cash flow diagram for this investment from Kitchener s perspective. 2. Calculate the amount of money in the money market fund on December 31, 2015, and prepare the journal entry necessary to recognize interest income. 3. Calculate the amount of money in the money market fund on December 31, 2016, and prepare the journal entry necessary to recognize interest income. Solution: 1. CORNERSTONE A12 (continued) Because we are calculating the value at 12/31/15, there is only one period: FV ¼ (f )(FV of a Single Amount, 1 period, 3%) ¼ ($200,000)(1:03) ¼ $206,000 The excess of the amount of money over the original deposit is the interest earned from July 1 through December 31, Dec. 31, 2015 Cash 6,000 Interest Income 6,000 (Record interest income) 3. FV ¼ (f )(FV of a Single Amount, 2 periods, 3%) ¼ ($206,000)(1:03 2 ) ¼ $218,545:40 Shareholders Equity Assets 5 Liabilities 1 (Interest Income) þ6,000 þ6,000 The interest income for the year is the increase in the amount of money during 2016, which is $12, ($218, $206,000). The journal entry to record interest income would be as follows: Dec. 31, 2016 Cash 12, Interest income 12, (Record interest income) Shareholders Equity Assets 5Liabilities1(Interest Income) þ12, þ12, Computing the Present Value of a Single Amount In computing the present value of a single amount, the following elements are used: f: the future cash flow PV: the present value n: the number of periods between the present time and the future cash flow i: the interest rate per period In present value problems, the interest rate is sometimes called the discount rate.
8 Appendix 1 Time Value of Money 705 To find the present value of a single amount, use the following equation: f PV ¼ (1 þ i) n You could use the present value table in Exhibit A18 (p. 718), where M 2 is the multiple from Exhibit A18 that corresponds to the appropriate values of n and i: PV ¼ (f )(M 2 ) Suppose Marathon Oil has purchased property on which it plans to develop oil wells. The seller has agreed to accept a single $150,000,000 payment three years from now, when Marathon expects to be selling oil from the field. Assuming an interest rate of 7% per year, the present value of the amount to be received in three years from the borrower s perspective can be calculated as shown in Exhibit A14. Present Value of a Single Amount: An Example Exhibit A14 The shortcut calculation, using the present value table (Exhibit A18, p. 718), would be as follows: PV ¼ (f )(M 2 ) ¼ ($150,000,000)(0:81630) ¼ $122,445,000 You can find M 2 at the intersection of the 7% column (i ¼ 7%) and the third row (n ¼ 3) in Exhibit A18 (p. 718) or by calculating [1/(1.07) 3 ]. This multiple is the present value of a $1 cash inflow or outflow in three years at 7%. Thus, the present value of $150,000,000 is $150,000,000 times the multiple. Although the future value calculation cannot be used to determine the present value, it can be used to verify that the present value calculated by using the table is correct. The following calculation is proof for the present value problem: Calculated present value (PV) $122,445,000 First year s interest ($122,445, ) 8,571,150 Loan payable at end of first year 131,016,150 Second year s interest ($131,016, ) 9,171,131 Loan payable at end of second year 140,187,281 Third year s interest ($140,187, ) 9,813,110 Loan payable at end of the third year (f ) $150,000,391 Again, the $391 difference between the amount here and the assumed $150,000,000 cash flow is due to rounding. When interest is compounded on the calculated present value of $122,445,000, then the present value calculation is reversed and we return to the future cash flow of $150,000,000. This reversal proves that $122,445,000 is the correct present value. CORNERSTONE A13 (p. 706) shows how to compute the present value of a single amount.
9 706 Appendix 1 Time Value of Money CORNERSTONE A13 Computing Present Value of a Single Amount Information: On October 1, 2015, Adelsman Manufacturing Company sold a new machine to Raul Inc. The machine represented a new design that Raul was eager to place in service. Since Raul was unable to pay for the machine on the date of purchase, Adelsman agreed to defer the $60,000 payment for 15 months. The appropriate rate of interest in such transactions is 8% per year compounded quarterly (2% per threemonth period). Why: The present value of a single cash flow is the original cash flow that must be invested to produce a known value at a specific future date. 1. Draw the cash flow diagram for this deferredpayment purchase from Raul s (the borrower s) perspective. 2. Calculate the present value of this deferredpayment purchase. 3. Prepare the journal entry necessary to record the acquisition of the machine. Solution: FV ¼ (f )(FV of a Single Amount, 5 periods, 2%) ¼ ($60,000)(0:90573) ¼ $54, Oct. 1, 2015 Equipment 54,344 Note Payable 54,344 (Record purchase of equipment) Assets 5 Liabilities 1 þ54,344 þ54,344 Shareholders Equity Computing the Future Value of an Annuity So far, we have been discussing problems that involve a single cash flow. However, there are also instances of multiple cash flows one period apart. An annuity is a number of equal cash flows: one to each interest period. For example, an investment in a security that pays $1,000 to an investor every December 31 for 10 consecutive years is an annuity. A loan repayment schedule that calls for a payment of $ on the first day of each month can also be considered an annuity. (Although the number of days in a month varies from 28 to 31, the interest period is defined as one month without regard to the number of days in each month.) In computing the future value of an annuity, the following elements are used: f : the amount of each repeating cash flow FV: the future value after the last (n th ) cash flow n: the number of cash flows i: the interest rate per period
10 Appendix 1 Time Value of Money 707 To find the future value of an annuity, use the following equation: FV ¼ (f ) (1 þ i)n 1 i Alternatively, you could use the future value table in Exhibit A19 (p. 719), where M 3 is the multiple from Exhibit A19 that corresponds to the appropriate values of n and i: FV ¼ (f )(M 3 ) Assume that CIBC wants to advertise a new savings program to its customers. The savings program requires the customers to make four annual payments of $5,000 each, with the first payment due three years before the program ends. CIBC advertises a 6% interest rate compounded annually. The future value of this annuity immediately after the fourth cash payment from the investor s perspective is shown in Exhibit A15. Future Value of an Annuity: An Example Exhibit A15 Note that the first period in Exhibit A15 is drawn with a dotted line. When using annuities, the timevalueofmoney model assumes that all cash flows occur at the end of a period. Therefore, the first cash flow in the future value of an annuity occurs at the end of the first period. However, since interest cannot be earned until the first deposit has been made, the first period is identified as a nointerest period. The future value (FV) can be computed as follows: Interest for first period ($0 3 6%) $ 0.00 First deposit 5, Investment balance at end of first year 5, Second year s interest ($5, ) Second deposit 5, Investment balance at end of second year 10, Third year s interest ($10, ) Third deposit 5, Investment balance at end of third year 15, Fourth year s interest ($15, ) Fourth deposit 5, Investment at end of fourth year $21, This calculation shows that the lender has accumulated a future value (FV) of $21, by the end of the fourth period, immediately after the fourth cash investment. The shortcut calculation, using the future value table (Exhibit A19, p. 719), would be as follows: FV ¼ (f )(M 3 ) ¼ ($5,000)(4:37462) ¼ $21,873
11 708 Appendix 1 Time Value of Money You can find M 3 at the intersection of the 6% column (i ¼ 6%) and the fourth row (n ¼ 4) in Exhibit A19 (p. 719) or by calculating ( )/0.06. This multiple is the future value of an annuity of four cash flows of $1 each at 6%. The future value of an annuity of $5,000 cash flows is $5,000 times the multiple. Thus, the table allows us to calculate the future value of an annuity by a single multiplication, no matter how many cash flows are involved. COR NERSTONE A14 shows how to compute the future value of an annuity. CORNERSTONE A14 Computing Future Value of an Annuity Information: Greg Smith is a lawyer and CA specializing in retirement and estate planning. One of Greg s clients, the owner of a large farm, wants to retire in five years. To provide funds to purchase a retirement annuity from London Life at the date of retirement, Greg asks the client to give him annual payments of $170,000, which Greg will deposit in a special fund that will earn 7% per year. Why: The future value of an annuity is the value of a series of equal cash flows made at regular intervals with compound interest at some specific future date. 1. Draw the cash flow diagram for the fund from Greg s client s perspective. 2. Calculate the future value of the fund immediately after the fifth deposit. 3. If Greg s client needs $1,000,000 to purchase the annuity, how much must be deposited every year? Solution: FV ¼ (f )(FV of an Annuity, 5periods, 7%) ¼ ($170,000)(5:75074) ¼ $977, In this case, the future value is known, but the annuity amount (f ) is not: 1,000,000 ¼ (f )(FV of an Annuity, 5 periods, 7%) 1,000,000 ¼ (f )(5:75074) f ¼ 1,000,000=5:75074 f ¼ $173,890:66 Present Value of an Annuity In computing the present value of an annuity, the following elements are used: f : the amount of each repeating cash flow PV: the present value of the n future cash flows n: the number of cash flows and periods i: the interest (or discount) rate per period
12 Appendix 1 Time Value of Money 709 To find the present value of an annuity, use the following equation: 1 1 (1 þ i) n PV ¼ (f ) i You could also use the present value table in Exhibit A110 (p. 720), where M 4 is the multiple from Exhibit A110 that corresponds to the appropriate values of n and i: PV ¼ (f )(M 4 ) For example, assume that Xerox Corporation purchased a new machine for its manufacturing operations. The purchase agreement requires Xerox to make four equally spaced payments of $24,154 each. The interest rate is 8% compounded annually and the first cash flow occurs one year after the purchase. Exhibit A16 shows how to determine the present value of this annuity from Xerox s (the borrower s) perspective. Note that the same concept applies to both the lender s and borrower s perspectives. Present Value of An Annuity: An Example Exhibit A16 The shortcut calculation, using the present value table (Exhibit A110, p. 720), would be as follows: PV ¼ (f )(M 4 ) ¼ ($24,154)(3:31213) ¼ $80,001:19 You can find M 4 at the intersection of the 8% column (i ¼ 8%) and the fourth row (n ¼ 4) in Exhibit A110 or by solving for [1 (1/ )]/0.08. This multiple is the present value of an annuity of four cash flows of $1 each at 8%. The present value of an annuity of four $24,154 cash flows is $24,154 times the multiple. Again, although the compound interest calculation is not used to determine the present value, it can be used to prove that the present value found using the table is correct. The following calculation verifies the present value in the problem: Calculated present value (PV) $ 80, Interest for first year ($80, ) 6, Less: First cash flow (24,154.00) Balance at end of first year 62, Interest for second year ($62, ) 4, Less: Second cash flow (24,154.00) Balance at end of second year 43, Interest for third year ($43, ) 3, Less: Third cash flow (24,154.00) Balance at end of third year 22, Interest for fourth year ($22, ) 1, Less: Fourth cash flow (24,154.00) Balance at end of fourth year $ 0.11 This proof uses a compound interest calculation that is the reverse of the present value formula. If the present value (PV) calculated with the formula is correct, then the proof
13 710 Appendix 1 Time Value of Money should end with a balance of zero immediately after the last cash flow. This proof ends with a balance of $0.11 because of rounding in the proof itself and in the table in Exhibit A110 (p. 720). CORNERSTONE A15 shows how to compute the present value of an annuity. CORNERSTONE A15 Computing Present Value of an Annuity Information: Windsor Builders purchased a subdivision site from the Royal Bank on January 1, Windsor gave the bank an installment note. The note requires Windsor to make four annual payments of $600,000 each on December 31 of each year, beginning in Interest is computed at 9%. Why: The present value of an annuity is the value of a series of equal future cash flows made at regular intervals with compound interest discounted back to today. 1. Draw the cash flow diagram for this purchase from Windsor s perspective. 2. Calculate the cost of the land as recorded by Windsor on January 1, Prepare the journal entry that Windsor will make to record the purchase of the land. Solution: PV ¼ (f )(PV of an Annuity, 4 periods, 9%) ¼ ($600,000)(3:23972) ¼ $1,943, Jan. 1, 2015 Land 1,943,832 Notes Payable 1,943,832 (Record purchase of land) Assets 5 Liabilities 1 Shareholders Equity þ1,943,832 þ1,943,832 SUMMARY OF LEARNING OBJECTIVES LO1. Explain how compound interest works. In transactions involving the borrowing and lending of money, it is customary for the borrower to pay interest. With compound interest, interest for the period is added to the account and interest is earned on the total balance in the next period. Compound interest calculations require careful specification of the interest period and the interest rate.
14 Appendix 1 Time Value of Money 711 LO2. Use future value and present value tables to apply compound interest to accounting transactions. Cash flows are described as either single cash flows, or annuities. An annuity is a number of equal cash flows made at regular intervals. All other cash flows are a series of one or more single cash flows. Accounting for such cash flows may require calculation of the amount to which a series of cash flows will grow when interest is compounded (i.e., the future value) or the amount a series of future cash flows is worth today after taking into account compound interest (i.e., the present value). CORNERSTONE A11 Computing future values using compound interest (p. 700) CORNERSTONE A12 Computing future value of a single amount (p. 703) CORNERSTONE A13 Computing present value of a single amount (p. 706) CORNERSTONE A14 Computing future value of an annuity (p. 708) CORNERSTONE A15 Computing present value of an annuity (p. 710) CORNERSTONES FOR APPENDIX 1 KEY TERMS Annuity (p. 706) Compound interest (p. 699) Future value (p. 700) Interest period (p. 699) Interest rate (p. 699) Present value (p. 701) Time value of money (p. 699) DISCUSSION QUESTIONS 1. Why does money have a time value? 2. Describe the four basic timevalueofmoney problems. 3. How is compound interest computed? What is a future value? What is a present value? 4. Define an annuity in general terms. Describe the cash flows related to an annuity from the viewpoint of the lender in terms of receipts and payments. 5. Explain how to use timevalueofmoney calculations to measure an installment note liability. CORNERSTONE EXERCISES Cornerstone Exercise A11 Explain How Compound Interest Works Jim Emig has $6,000. OBJECTIVE 1 CORNERSTONE A11 Calculate the future value of the $6,000 at 12% compounded quarterly for five years. (Note: Round answers to two decimal places.)
15 CORNERSTONE A12 Cornerstone Exercise A12 Use Future Value and Present Value Tables to Apply Compound Interest Cathy Lumbattis inherited $140,000 from an aunt. 712 Appendix 1 Time Value of Money CORNERSTONE A13 CORNERSTONE A13 CORNERSTONE A14 CORNERSTONE A14 CORNERSTONE A14 CORNERSTONE A14 If Cathy decides not to spend her inheritance but to leave the money in her savings account until she retires in 15 years, how much money will she have, assuming an annual interest rate of 8%, compounded semiannually? (Note: Round answers to two decimal places.) Cornerstone Exercise A13 Use Future Value and Present Value Tables to Apply Compound Interest LuAnn Bean will receive $7,000 in seven years. What is the present value at 7% compounded annually? (Note: Round answers to two decimal places.) Cornerstone Exercise A14 Use Future Value and Present Value Tables to Apply Compound Interest A bank is willing to lend money at 6% interest, compounded annually. How much would the bank be willing to loan you in exchange for a payment of $600 four years from now? (Note: Round answers to two decimal places.) Cornerstone Exercise A15 Use Future Value and Present Value Tables to Apply Compound Interest Ed Flores wants to save some money so that he can make a down payment of $3,000 on a car when he graduates from university in four years. If Ed opens a savings account and earns 3% on his money, compounded annually, how much will he have to invest now? (Note: Round answers to two decimal places.) Cornerstone Exercise A16 Use Future Value and Present Value Tables to Apply Compound Interest Kristen Lee makes equal deposits of $500 semiannually for four years. What is the future value at 8%? (Note: Round answers to two decimal places.) Cornerstone Exercise A17 Use Future Value and Present Value Tables to Apply Compound Interest Chuck Russo, a high school math teacher, wants to set up a RRSP account into which he will deposit $2,000 per year. He plans to teach for 20 more years and then retire. If the interest on his account is 7% compounded annually, how much will be in his account when he retires? (Note: Round answers to two decimal places.) Cornerstone Exercise A18 Use Future Value Tables to Apply Compound Interest Larson Lumber makes annual deposits of $500 at 6% compounded annually for three years. What is the future value of these deposits? (Note: Round answers to two decimal places.)
16 Appendix 1 Time Value of Money 713 Cornerstone Exercise A19 Use Future Value and Present Value Tables to Apply Compound Interest Michelle Legrand can earn 6%. How much would have to be deposited in a savings account today in order for Michelle to be able to make equal annual withdrawals of $200 at the end of each of the next 10 years? (Note: Round answers to two decimal places.) The balance at the end of the last year would be zero. Cornerstone Exercise A110 Use Future Value and Present Value Tables to Apply Compound Interest Barb Muller wins the lottery. She wins $20,000 per year to be paid for 10 years. The province offers her the choice of a cash settlement now instead of the annual payments for 10 years. CORNERSTONE A15 CORNERSTONE A15 If the interest rate is 6%, what is the amount the province will offer for a settlement today? (Note: Round answers to two decimal places.) EXERCISES Exercise A111 Practice with Tables Refer to the appropriate tables in the text. Note: Round answers to two decimal places. Determine: a. the future value of a single cash flow of $5,000 that earns 7% interest compounded annually for 10 years. b. the future value of an annual annuity of 10 cash flows of $500 each that earns 7% compounded annually. c. the present value of $5,000 to be received 10 years from now, assuming that the interest (discount) rate is 7% per year. d. the present value of an annuity of $500 per year for 10 years for which the interest (discount) rate is 7% per year and the first cash flow occurs one year from now. Exercise A112 Practice with Tables Refer to the appropriate tables in the text. Note: Round answers to two decimal places. Determine: a. the present value of $1,200 to be received in seven years, assuming that the interest (discount) rate is 8% per year. b. the present value of an annuity of seven cash flows of $1,200 each (one at the end of each of the next seven years) for which the interest (discount) rate is 8% per year. c. the future value of a single cash flow of $1,200 that earns 8% per year for seven years. d. the future value of an annuity of seven cash flows of $1,200 each (one at the end of each of the next seven years), assuming that the interest rate is 8% per year. Exercise A113 Future Values Refer to the appropriate tables in the text. Note: Round answers to two decimal places. Determine: a. the future value of a single deposit of $15,000 that earns compound interest for four years at an interest rate of 10% per year. b. the annual interest rate that will produce a future value of $13, in six years from a single deposit of $8,000.
17 714 Appendix 1 Time Value of Money c. the size of annual cash flows for an annuity of nine cash flows that will produce a future value of $79, at an interest rate of 9% per year. d. the number of periods required to produce a future value of $17, from an initial deposit of $7,500 if the annual interest rate is 9%. Exercise A114 Future Values and LongTerm Investments Fired Up Pottery Inc. engaged in the following transactions during 2015: a. On January 1, 2015, Fired Up deposited $12,000 in a certificate of deposit paying 6% interest compounded semiannually (3% per sixmonth period). The certificate will mature on December 31, b. On January 1, 2015, Fired Up established an account with Rookwood Investment Management. Fired Up will make quarterly payments of $2,500 to Rookwood beginning on March 31, 2015, and ending on December 31, Rookwood guarantees an interest rate of 8% compounded quarterly (2% per threemonth period). 1. Prepare the cash flow diagram for each of these two investments. 2. Calculate the amount to which each of these investments will accumulate at maturity. (Note: Round answers to two decimal places.) Exercise A115 Future Values On January 1, Beth Walid made a single deposit of $8,000 in an investment account that earns 8% interest. Note: Round answers to two decimal places. 1. Calculate the balance in the account in five years assuming the interest is compounded annually. 2. Determine how much interest will be earned on the account in seven years if interest is compounded annually. 3. Calculate the balance in the account in five years assuming the 8% interest is compounded quarterly. Exercise A116 Future Values Kashmir Transit Company invested $70,000 in a corporate bond on June 30, The bond earns 12% interest compounded monthly (1% per month) and matures on March 31, Note: Round answers to two decimal places. 1. Prepare the cash flow diagram for this investment. 2. Determine the amount Kashmir will receive when the bond matures. 3. Determine how much interest Kashmir will earn on this investment from June 30, 2015, through December 31, Exercise A117 Present Values Refer to the appropriate tables in the text. Note: Round answers to two decimal places. Determine: a. the present value of a single $14,000 cash flow in seven years if the interest (discount) rate is 8% per year. b. the number of periods for which $5,820 must be invested at an annual interest (discount) rate of 7% to produce an investment balance of $10,000. c. the size of the annual cash flow for a 25year annuity with a present value of $49,113 and an annual interest rate of 9%. One payment is made at the end of each year. d. the annual interest rate at which an investment of $2,542 will provide for a single $4,000 cash flow in four years. e. the annual interest rate earned by an annuity that costs $17,119 and provides 15 payments of $2,000 each, one at the end of each of the next 15 years.
18 Appendix 1 Time Value of Money 715 Exercise A118 Present Values Weinstein Company signed notes to make the following two purchases on January 1, 2015: a. a new piece of equipment for $60,000, with payment deferred until December 31, The appropriate interest rate is 9% compounded annually. b. a small building from Johnston Builders. The terms of the purchase require a $75,000 payment at the end of each quarter, beginning March 31, 2015, and ending June 30, The appropriate interest rate is 2% per quarter. Note: Round answers to two decimal places. 1. Prepare the cash flow diagrams for these two purchases. 2. Prepare the entries to record these purchases in Weinstein s journal. 3. Prepare the cash payment and interest expense entries for purchase b at March 31, 2015, and June 30, Prepare the adjusting entry for purchase a at December 31, Exercise A119 Present Values Krista Kellman has an opportunity to purchase a government security that will pay $200,000 in five years. Note: Round answers to two decimal places. 1. Calculate what Krista would pay for the security if the appropriate interest (discount) rate is 6% compounded annually. 2. Calculate what Krista would pay for the security if the appropriate interest (discount) rate is 10% compounded annually. 3. Calculate what Krista would pay for the security if the appropriate interest (discount) rate is 6% compounded semiannually. Exercise A120 Future Values of an Annuity On December 31, 2015, Natalie Livingston signs a contract to make annual deposits of $4,200 in an investment account that earns 10%. The first deposit is made on December 31, Note: Round answers to two decimal places. 1. Calculate what the balance in this investment account will be just after the seventh deposit has been made if interest is compounded annually. 2. Determine how much interest will have been earned on this investment account just after the seventh deposit has been made if interest is compounded annually. Exercise A121 Future Values of an Annuity Essex Savings Bank pays 8% interest compounded weekly (0.154% per week) on savings accounts. The bank has asked your help in preparing a table to show potential customers the number of dollars that will be available at the end of 10, 20, 30, and 40week periods during which there are weekly deposits of $1, $5, $10, or $50. The following data are available: Length of Annuity Future Value of Annuity at an Interest Rate of 0.154% per Week 10 weeks weeks weeks weeks
19 716 Appendix 1 Time Value of Money Complete a table similar to the one below. (Note: Round answers to two decimal places.) Amount of Each Deposit Number of Deposits $1 $5 $10 $ Exercise A122 Future Value of a Single Cash Flow Jimenez Products has just been paid $25,000 by Shirley Enterprises, which has owed Jimenez this amount for 30 months but been unable to pay because of financial difficulties. Had it been able to invest this cash, Jimenez assumes that it would have earned an interest rate of 12% compounded monthly (1% per month). Note: Round answers to two decimal places. 1. Prepare a cash flow diagram for the investment that could have been made if Shirley had paid 30 months ago. 2. Determine how much Jimenez has lost by not receiving the $25,000 when it was due 30 months ago. 3. Conceptual Connection: Indicate whether Jimenez would make an entry to account for this loss. Why, or why not? Exercise A123 Installment Sale Wilke Properties owns land on which natural gas wells are located. Windsor Gas Company signs a note to buy this land from Wilke on January 1, The note requires Windsor to pay Wilke $775,000 per year for 25 years. The first payment is to be made on December 31, The appropriate interest rate is 9% compounded annually. Note: Round answers to two decimal places. 1. Prepare a diagram of the appropriate cash flows from Windsor Gas s perspective. 2. Determine the present value of the payments. 3. Indicate what entry Windsor Gas should make at January 1, Exercise A124 Installment Sale Bailey s Billiards sold a pool table to Sheri Sipka on October 31, The terms of the sale are no money down and payments of $50 per month for 30 months, with the first payment due on November 30, The table they sold to Sipka cost Bailey s $800, and Bailey uses a perpetual inventory system. Bailey s uses an interest rate of 12% compounded monthly (1% per month). Note: Round answers to two decimal places. 1. Prepare the cash flow diagram for this sale. 2. Calculate the amount of revenue Bailey s should record on October 31, Prepare the journal entries to record the sale on October 31. Assume that Bailey s records cost of goods sold at the time of the sale (perpetual inventory accounting). 4. Determine how much interest income Bailey s will record from October 31, 2015, through December 31, Determine how much Bailey s 2015 income before taxes increased from this sale.
20 Appendix 1 Time Value of Money 717 Exhibit A17 Future Value of a Single Amount FV ¼ 1(1 þ i) n n/i 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 18% 20% 25% 30%
21 718 Appendix 1 Time Value of Money Exhibit A18 Present Value of a Single Amount PV ¼ 1 (1þi) n n/i 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 12% 14% 16% 18% 20% 25% 30%
APPENDIX. Interest Concepts of Future and Present Value. Concept of Interest TIME VALUE OF MONEY BASIC INTEREST CONCEPTS
CHAPTER 8 Current Monetary Balances 395 APPENDIX Interest Concepts of Future and Present Value TIME VALUE OF MONEY In general business terms, interest is defined as the cost of using money over time. Economists
More informationTimeValueofMoney and Amortization Worksheets
2 TimeValueofMoney and Amortization Worksheets The TimeValueofMoney and Amortization worksheets are useful in applications where the cash flows are equal, evenly spaced, and either all inflows or
More informationPresent Value (PV) Tutorial
EYK 151 Present Value (PV) Tutorial The concepts of present value are described and applied in Chapter 15. This supplement provides added explanations, illustrations, calculations, present value tables,
More information3. Time value of money. We will review some tools for discounting cash flows.
1 3. Time value of money We will review some tools for discounting cash flows. Simple interest 2 With simple interest, the amount earned each period is always the same: i = rp o where i = interest earned
More informationProblem Set: Annuities and Perpetuities (Solutions Below)
Problem Set: Annuities and Perpetuities (Solutions Below) 1. If you plan to save $300 annually for 10 years and the discount rate is 15%, what is the future value? 2. If you want to buy a boat in 6 years
More informationTime Value of Money CAP P2 P3. Appendix. Learning Objectives. Conceptual. Procedural
Appendix B Time Value of Learning Objectives CAP Conceptual C1 Describe the earning of interest and the concepts of present and future values. (p. B1) Procedural P1 P2 P3 P4 Apply present value concepts
More informationPresent Value Concepts
Present Value Concepts Present value concepts are widely used by accountants in the preparation of financial statements. In fact, under International Financial Reporting Standards (IFRS), these concepts
More informationICASL  Business School Programme
ICASL  Business School Programme Quantitative Techniques for Business (Module 3) Financial Mathematics TUTORIAL 2A This chapter deals with problems related to investing money or capital in a business
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 6
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17, 19 2. Use
More informationTime Value of Money. Nature of Interest. appendix. study objectives
2918T_appC_C01C20.qxd 8/28/08 9:57 PM Page C1 appendix C Time Value of Money study objectives After studying this appendix, you should be able to: 1 Distinguish between simple and compound interest.
More informationTVM Applications Chapter
Chapter 6 Time of Money UPS, Walgreens, Costco, American Air, Dreamworks Intel (note 10 page 28) TVM Applications Accounting issue Chapter Notes receivable (longterm receivables) 7 Longterm assets 10
More information14 ARITHMETIC OF FINANCE
4 ARITHMETI OF FINANE Introduction Definitions Present Value of a Future Amount Perpetuity  Growing Perpetuity Annuities ompounding Agreement ontinuous ompounding  Lump Sum  Annuity ompounding Magic?
More information5.1 Simple and Compound Interest
5.1 Simple and Compound Interest Question 1: What is simple interest? Question 2: What is compound interest? Question 3: What is an effective interest rate? Question 4: What is continuous compound interest?
More informationAppendix C 1. Time Value of Money. Appendix C 2. Financial Accounting, Fifth Edition
C 1 Time Value of Money C 2 Financial Accounting, Fifth Edition Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount. 3. Solve for future
More informationTime Value of Money 1
Time Value of Money 1 This topic introduces you to the analysis of tradeoffs over time. Financial decisions involve costs and benefits that are spread over time. Financial decision makers in households
More informationChapter 4. Time Value of Money
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationThe Time Value of Money
C H A P T E R6 The Time Value of Money When plumbers or carpenters tackle a job, they begin by opening their toolboxes, which hold a variety of specialized tools to help them perform their jobs. The financial
More informationChapter 6. Time Value of Money Concepts. Simple Interest 61. Interest amount = P i n. Assume you invest $1,000 at 6% simple interest for 3 years.
61 Chapter 6 Time Value of Money Concepts 62 Time Value of Money Interest is the rent paid for the use of money over time. That s right! A dollar today is more valuable than a dollar to be received in
More informationChapter The Time Value of Money
Chapter The Time Value of Money PPT 92 Chapter 9  Outline Time Value of Money Future Value and Present Value Annuities TimeValueofMoney Formulas Adjusting for NonAnnual Compounding Compound Interest
More informationSample Examination Questions CHAPTER 6 ACCOUNTING AND THE TIME VALUE OF MONEY MULTIPLE CHOICE Conceptual Answer No. Description d 1. Definition of present value. c 2. Understanding compound interest tables.
More informationCHAPTER 6 DISCOUNTED CASH FLOW VALUATION
CHAPTER 6 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. The four pieces are the present value (PV), the periodic cash flow (C), the discount rate (r), and
More informationFin 5413 CHAPTER FOUR
Slide 1 Interest Due Slide 2 Fin 5413 CHAPTER FOUR FIXED RATE MORTGAGE LOANS Interest Due is the mirror image of interest earned In previous finance course you learned that interest earned is: Interest
More informationCHAPTER 6. Accounting and the Time Value of Money. 2. Use of tables. 13, 14 8 1. a. Unknown future amount. 7, 19 1, 5, 13 2, 3, 4, 7
CHAPTER 6 Accounting and the Time Value of Money ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC) Topics Questions Brief Exercises Exercises Problems 1. Present value concepts. 1, 2, 3, 4, 5, 9, 17 2. Use of
More informationTime Value of Money. 2014 Level I Quantitative Methods. IFT Notes for the CFA exam
Time Value of Money 2014 Level I Quantitative Methods IFT Notes for the CFA exam Contents 1. Introduction...2 2. Interest Rates: Interpretation...2 3. The Future Value of a Single Cash Flow...4 4. The
More informationChapter 6. Discounted Cash Flow Valuation. Key Concepts and Skills. Multiple Cash Flows Future Value Example 6.1. Answer 6.1
Chapter 6 Key Concepts and Skills Be able to compute: the future value of multiple cash flows the present value of multiple cash flows the future and present value of annuities Discounted Cash Flow Valuation
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL738 Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationAppendix. Time Value of Money. Financial Accounting, IFRS Edition Weygandt Kimmel Kieso. Appendix C 1
C Time Value of Money C 1 Financial Accounting, IFRS Edition Weygandt Kimmel Kieso C 2 Study Objectives 1. Distinguish between simple and compound interest. 2. Solve for future value of a single amount.
More informationSolutions to Time value of money practice problems
Solutions to Time value of money practice problems Prepared by Pamela Peterson Drake 1. What is the balance in an account at the end of 10 years if $2,500 is deposited today and the account earns 4% interest,
More informationStatistical Models for Forecasting and Planning
Part 5 Statistical Models for Forecasting and Planning Chapter 16 Financial Calculations: Interest, Annuities and NPV chapter 16 Financial Calculations: Interest, Annuities and NPV Outcomes Financial information
More informationFinQuiz Notes 2 0 1 5
Reading 5 The Time Value of Money Money has a time value because a unit of money received today is worth more than a unit of money to be received tomorrow. Interest rates can be interpreted in three ways.
More informationREVIEW MATERIALS FOR REAL ESTATE ANALYSIS
REVIEW MATERIALS FOR REAL ESTATE ANALYSIS 1997, Roy T. Black REAE 5311, Fall 2005 University of Texas at Arlington J. Andrew Hansz, Ph.D., CFA CONTENTS ITEM ANNUAL COMPOUND INTEREST TABLES AT 10% MATERIALS
More informationInterest Rate and Credit Risk Derivatives
Interest Rate and Credit Risk Derivatives Interest Rate and Credit Risk Derivatives Peter Ritchken Kenneth Walter Haber Professor of Finance Weatherhead School of Management Case Western Reserve University
More informationPREVIEW OF CHAPTER 62
61 PREVIEW OF CHAPTER 6 62 Intermediate Accounting IFRS 2nd Edition Kieso, Weygandt, and Warfield 6 Accounting and the Time Value of Money LEARNING OBJECTIVES After studying this chapter, you should
More informationThe Concept of Present Value
The Concept of Present Value If you could have $100 today or $100 next week which would you choose? Of course you would choose the $100 today. Why? Hopefully you said because you could invest it and make
More informationInvestigating Investment Formulas Using Recursion Grade 11
Ohio Standards Connection Patterns, Functions and Algebra Benchmark C Use recursive functions to model and solve problems; e.g., home mortgages, annuities. Indicator 1 Identify and describe problem situations
More informationRegular Annuities: Determining Present Value
8.6 Regular Annuities: Determining Present Value GOAL Find the present value when payments or deposits are made at regular intervals. LEARN ABOUT the Math Harry has money in an account that pays 9%/a compounded
More informationFinding the Payment $20,000 = C[1 1 / 1.0066667 48 ] /.0066667 C = $488.26
Quick Quiz: Part 2 You know the payment amount for a loan and you want to know how much was borrowed. Do you compute a present value or a future value? You want to receive $5,000 per month in retirement.
More informationYou just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
More informationLO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs.
LO.a: Interpret interest rates as required rates of return, discount rates, or opportunity costs. 1. The minimum rate of return that an investor must receive in order to invest in a project is most likely
More informationTime value of money. appendix B NATURE OF INTEREST
appendix B Time value of money LEARNING OBJECTIVES After studying this appendix, you should be able to: Distinguish between simple and compound interest. Solve for future value of a single amount. Solve
More informationModule 8: Current and longterm liabilities
Module 8: Current and longterm liabilities Module 8: Current and longterm liabilities Overview In previous modules, you learned how to account for assets. Assets are what a business uses or sells to
More informationTime Value of Money. 15.511 Corporate Accounting Summer 2004. Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology
Time Value of Money 15.511 Corporate Accounting Summer 2004 Professor S. P. Kothari Sloan School of Management Massachusetts Institute of Technology July 2, 2004 1 LIABILITIES: Current Liabilities Obligations
More informationCALCULATOR TUTORIAL. Because most students that use Understanding Healthcare Financial Management will be conducting time
CALCULATOR TUTORIAL INTRODUCTION Because most students that use Understanding Healthcare Financial Management will be conducting time value analyses on spreadsheets, most of the text discussion focuses
More informationAPPENDIX 3 TIME VALUE OF MONEY. Time Lines and Notation. The Intuitive Basis for Present Value
1 2 TIME VALUE OF MONEY APPENDIX 3 The simplest tools in finance are often the most powerful. Present value is a concept that is intuitively appealing, simple to compute, and has a wide range of applications.
More informationBasic Concept of Time Value of Money
Basic Concept of Time Value of Money CHAPTER 1 1.1 INTRODUCTION Money has time value. A rupee today is more valuable than a year hence. It is on this concept the time value of money is based. The recognition
More informationChapter 6. Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams
Chapter 6 Learning Objectives Principles Used in This Chapter 1. Annuities 2. Perpetuities 3. Complex Cash Flow Streams 1. Distinguish between an ordinary annuity and an annuity due, and calculate present
More informationThe time value of money: Part II
The time value of money: Part II A reading prepared by Pamela Peterson Drake O U T L I E 1. Introduction 2. Annuities 3. Determining the unknown interest rate 4. Determining the number of compounding periods
More informationCHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY
CHAPTER 5 INTRODUCTION TO VALUATION: THE TIME VALUE OF MONEY Answers to Concepts Review and Critical Thinking Questions 1. The four parts are the present value (PV), the future value (FV), the discount
More informationMGF 1107 Spring 11 Ref: 606977 Review for Exam 2. Write as a percent. 1) 3.1 1) Write as a decimal. 4) 60% 4) 5) 0.085% 5)
MGF 1107 Spring 11 Ref: 606977 Review for Exam 2 Mr. Guillen Exam 2 will be on 03/02/11 and covers the following sections: 8.1, 8.2, 8.3, 8.4, 8.5, 8.6. Write as a percent. 1) 3.1 1) 2) 1 8 2) 3) 7 4 3)
More information1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%?
Chapter 2  Sample Problems 1. If you wish to accumulate $140,000 in 13 years, how much must you deposit today in an account that pays an annual interest rate of 14%? 2. What will $247,000 grow to be in
More informationModule 5: Interest concepts of future and present value
file:///f /Courses/201011/CGA/FA2/06course/m05intro.htm Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present
More information1.3.2015 г. D. Dimov. Year Cash flow 1 $3,000 2 $5,000 3 $4,000 4 $3,000 5 $2,000
D. Dimov Most financial decisions involve costs and benefits that are spread out over time Time value of money allows comparison of cash flows from different periods Question: You have to choose one of
More informationCalculator and QuickCalc USA
Investit Software Inc. www.investitsoftware.com. Calculator and QuickCalc USA TABLE OF CONTENTS Steps in Using the Calculator Time Value on Money Calculator Is used for compound interest calculations involving
More informationWith compound interest you earn an additional $128.89 ($1628.89  $1500).
Compound Interest Interest is the amount you receive for lending money (making an investment) or the fee you pay for borrowing money. Compound interest is interest that is calculated using both the principle
More information1. Annuity a sequence of payments, each made at equally spaced time intervals.
Ordinary Annuities (Young: 6.2) In this Lecture: 1. More Terminology 2. Future Value of an Ordinary Annuity 3. The Ordinary Annuity Formula (Optional) 4. Present Value of an Ordinary Annuity More Terminology
More informationThe Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820)
The Mathematics of Financial Planning (supplementary lesson notes to accompany FMGT 2820) Using the Sharp EL733A Calculator Reference is made to the Appendix Tables A1 to A4 in the course textbook Investments:
More informationFinance CHAPTER OUTLINE. 5.1 Interest 5.2 Compound Interest 5.3 Annuities; Sinking Funds 5.4 Present Value of an Annuity; Amortization
CHAPTER 5 Finance OUTLINE Even though you re in college now, at some time, probably not too far in the future, you will be thinking of buying a house. And, unless you ve won the lottery, you will need
More informationModule 5: Interest concepts of future and present value
Page 1 of 23 Module 5: Interest concepts of future and present value Overview In this module, you learn about the fundamental concepts of interest and present and future values, as well as ordinary annuities
More informationChapter 4. Time Value of Money. Copyright 2009 Pearson Prentice Hall. All rights reserved.
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationChapter 4. Time Value of Money. Learning Goals. Learning Goals (cont.)
Chapter 4 Time Value of Money Learning Goals 1. Discuss the role of time value in finance, the use of computational aids, and the basic patterns of cash flow. 2. Understand the concept of future value
More informationThe Time Value of Money
The following is a review of the Quantitative Methods: Basic Concepts principles designed to address the learning outcome statements set forth by CFA Institute. This topic is also covered in: The Time
More informationStandard Mortgage Terms
Page 1 of 45 Standard Mortgage Terms Filed By: Canadian Imperial Bank of Commerce Filing Number: MT160006 Filing Date: March 17, 2016 The following set of standard mortgage terms shall be deemed to be
More informationTopics Covered. Compounding and Discounting Single Sums. Ch. 4  The Time Value of Money. The Time Value of Money
Ch. 4  The Time Value of Money Topics Covered Future Values Present Values Multiple Cash Flows Perpetuities and Annuities Effective Annual Interest Rate For now, we will omit the section 4.5 on inflation
More informationIt Is In Your Interest
STUDENT MODULE 7.2 BORROWING MONEY PAGE 1 Standard 7: The student will identify the procedures and analyze the responsibilities of borrowing money. It Is In Your Interest Jason did not understand how it
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Answers to Concepts Review and Critical Thinking Questions 1. Assuming positive cash flows and interest rates, the future value increases and the present value
More informationActivity 3.1 Annuities & Installment Payments
Activity 3.1 Annuities & Installment Payments A Tale of Twins Amy and Amanda are identical twins at least in their external appearance. They have very different investment plans to provide for their retirement.
More informationTop 50 Banking Interview Questions
Top 50 Banking Interview Questions 1) What is bank? What are the types of banks? A bank is a financial institution licensed as a receiver of cash deposits. There are two types of banks, commercial banks
More information10.3 Future Value and Present Value of an Ordinary General Annuity
360 Chapter 10 Annuities 10.3 Future Value and Present Value of an Ordinary General Annuity 29. In an ordinary general annuity, payments are made at the end of each payment period and the compounding period
More informationVOCABULARY INVESTING Student Worksheet
Vocabulary Worksheet Page 1 Name Period VOCABULARY INVESTING Student Worksheet PRIMARY VOCABULARY 1. Savings: 2. Investments: 3. Investing: 4. Risk: 5. Return: 6. Liquidity: 7. Stocks: 8. Bonds: 9. Mutual
More information380.760: Corporate Finance. Financial Decision Making
380.760: Corporate Finance Lecture 2: Time Value of Money and Net Present Value Gordon Bodnar, 2009 Professor Gordon Bodnar 2009 Financial Decision Making Finance decision making is about evaluating costs
More informationAdditional Terms and Conditions
Page 1 of 35 Additional Terms and Conditions The following set of additional terms and conditions is attached as Schedule B to Canadian Imperial Bank of Commerce Residential Mortgages in Newfoundland and
More informationChapter 5 Time Value of Money 2: Analyzing Annuity Cash Flows
1. Future Value of Multiple Cash Flows 2. Future Value of an Annuity 3. Present Value of an Annuity 4. Perpetuities 5. Other Compounding Periods 6. Effective Annual Rates (EAR) 7. Amortized Loans Chapter
More informationAccounting Building Business Skills. Interest. Interest. Paul D. Kimmel. Appendix B: Time Value of Money
Accounting Building Business Skills Paul D. Kimmel Appendix B: Time Value of Money PowerPoint presentation by Kate WynnWilliams University of Otago, Dunedin 2003 John Wiley & Sons Australia, Ltd 1 Interest
More informationWhat You ll Learn. And Why. Key Words. interest simple interest principal amount compound interest compounding period present value future value
What You ll Learn To solve problems involving compound interest and to research and compare various savings and investment options And Why Knowing how to save and invest the money you earn will help you
More informationChapter 4: Net Present Value
4.1 a. Future Value = C 0 (1+r) T Chapter 4: Net Present Value = $1,000 (1.05) 10 = $1,628.89 b. Future Value = $1,000 (1.07) 10 = $1,967.15 c. Future Value = $1,000 (1.05) 20 = $2,653.30 d. Because interest
More informationCalculations for Time Value of Money
KEATMX01_p001008.qxd 11/4/05 4:47 PM Page 1 Calculations for Time Value of Money In this appendix, a brief explanation of the computation of the time value of money is given for readers not familiar with
More informationChapter 2. CASH FLOW Objectives: To calculate the values of cash flows using the standard methods.. To evaluate alternatives and make reasonable
Chapter 2 CASH FLOW Objectives: To calculate the values of cash flows using the standard methods To evaluate alternatives and make reasonable suggestions To simulate mathematical and real content situations
More informationFinite Mathematics. CHAPTER 6 Finance. Helene Payne. 6.1. Interest. savings account. bond. mortgage loan. auto loan
Finite Mathematics Helene Payne CHAPTER 6 Finance 6.1. Interest savings account bond mortgage loan auto loan Lender Borrower Interest: Fee charged by the lender to the borrower. Principal or Present Value:
More informationDISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS
Chapter 5 DISCOUNTED CASH FLOW VALUATION and MULTIPLE CASH FLOWS The basic PV and FV techniques can be extended to handle any number of cash flows. PV with multiple cash flows: Suppose you need $500 one
More information5. Time value of money
1 Simple interest 2 5. Time value of money With simple interest, the amount earned each period is always the same: i = rp o We will review some tools for discounting cash flows. where i = interest earned
More informationDick Schwanke Finite Math 111 Harford Community College Fall 2013
Annuities and Amortization Finite Mathematics 111 Dick Schwanke Session #3 1 In the Previous Two Sessions Calculating Simple Interest Finding the Amount Owed Computing Discounted Loans Quick Review of
More informationChapter F: Finance. Section F.1F.4
Chapter F: Finance Section F.1F.4 F.1 Simple Interest Suppose a sum of money P, called the principal or present value, is invested for t years at an annual simple interest rate of r, where r is given
More informationIntroduction to Real Estate Investment Appraisal
Introduction to Real Estate Investment Appraisal Maths of Finance Present and Future Values Pat McAllister INVESTMENT APPRAISAL: INTEREST Interest is a reward or rent paid to a lender or investor who has
More informationReal Estate. Refinancing
Introduction This Solutions Handbook has been designed to supplement the HP2C Owner's Handbook by providing a variety of applications in the financial area. Programs and/or stepbystep keystroke procedures
More informationCHAPTER 4 DISCOUNTED CASH FLOW VALUATION
CHAPTER 4 DISCOUNTED CASH FLOW VALUATION Solutions to Questions and Problems NOTE: Allendof chapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability
More informationCHAPTER 8 INTEREST RATES AND BOND VALUATION
CHAPTER 8 INTEREST RATES AND BOND VALUATION Solutions to Questions and Problems 1. The price of a pure discount (zero coupon) bond is the present value of the par value. Remember, even though there are
More informationStandard Charge Terms Land Registration Reform Act
Page 1 of 32 Standard Charge Terms Land Registration Reform Act Filed By: Canadian Imperial Bank of Commerce Filing Number: 201610 Filing Date: March 29, 2016 The following set of standard charge terms
More informationAnnuities and Sinking Funds
Annuities and Sinking Funds Sinking Fund A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of compounded
More informationThe Time Value of Money C H A P T E R N I N E
The Time Value of Money C H A P T E R N I N E Figure 91 Relationship of present value and future value PPT 91 $1,000 present value $ 10% interest $1,464.10 future value 0 1 2 3 4 Number of periods Figure
More informationCompound Interest. Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate:
Compound Interest Invest 500 that earns 10% interest each year for 3 years, where each interest payment is reinvested at the same rate: Table 1 Development of Nominal Payments and the Terminal Value, S.
More informationSuggested solutions to 3mark and 4mark problems contained in the Sample Paper  Exam 4: Tax Planning & Estate Planning
Suggested solutions to 3mark and 4mark problems contained in the Sample Paper  Exam 4: Tax Planning & Estate Planning Section II Question 6 Mrs. A whose date of birth is 30th March 1955 has a total
More informationMGT201 Lecture No. 07
MGT201 Lecture No. 07 Learning Objectives: After going through this lecture, you would be able to have an understanding of the following concepts. Discounted Cash Flows (DCF Analysis) Annuities Perpetuity
More informationTIME VALUE OF MONEY (TVM)
TIME VALUE OF MONEY (TVM) INTEREST Rate of Return When we know the Present Value (amount today), Future Value (amount to which the investment will grow), and Number of Periods, we can calculate the rate
More informationExercise 6 8. Exercise 6 12 PVA = $5,000 x 4.35526* = $21,776
CHAPTER 6: EXERCISES Exercise 6 2 1. FV = $10,000 (2.65330 * ) = $26,533 * Future value of $1: n = 20, i = 5% (from Table 1) 2. FV = $10,000 (1.80611 * ) = $18,061 * Future value of $1: n = 20, i = 3%
More informationSHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Ch. 5 Mathematics of Finance 5.1 Compound Interest SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 1) What is the effective
More informationThe Basics of Interest Theory
Contents Preface 3 The Basics of Interest Theory 9 1 The Meaning of Interest................................... 10 2 Accumulation and Amount Functions............................ 14 3 Effective Interest
More informationChapter 6 Contents. Principles Used in Chapter 6 Principle 1: Money Has a Time Value.
Chapter 6 The Time Value of Money: Annuities and Other Topics Chapter 6 Contents Learning Objectives 1. Distinguish between an ordinary annuity and an annuity due, and calculate present and future values
More informationPreparing cash budgets
3 Preparing cash budgets this chapter covers... In this chapter we will examine in detail how a cash budget is prepared. This is an important part of your studies, and you will need to be able to prepare
More information2 The Mathematics. of Finance. Copyright Cengage Learning. All rights reserved.
2 The Mathematics of Finance Copyright Cengage Learning. All rights reserved. 2.3 Annuities, Loans, and Bonds Copyright Cengage Learning. All rights reserved. Annuities, Loans, and Bonds A typical definedcontribution
More informationTime Value of Money. Work book Section I True, False type questions. State whether the following statements are true (T) or False (F)
Time Value of Money Work book Section I True, False type questions State whether the following statements are true (T) or False (F) 1.1 Money has time value because you forgo something certain today for
More information