Math of Finance Semester 1 Unit 2 Page 1 of 19

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1 Math of Finance Semester 1 Unit 2 Page 1 of 19 Name: Date: Unit 2.1 Checking Accounts Use your book or the internet to find the following definitions: Account balance: Deposit: Withdrawal: Direct deposit: ETF: Insufficient funds: Maintenance fee: ATM fees: Juliane has a balance of $1350 in her checking account. She deposits a check for $ and withdraws $200. What is her balance after the transactions? $ The account balance is $ after the transactions. 1. Your checking account balance is $ If you deposit 3 checks for $50, $56.14 and $ and withdraw $100 in cash, what is your new account balance? 2. Your checking account balance is $ If you deposit a check for $50 what is the maximum amount you can withdraw from your checking account without over-drafting your account?

2 Math of Finance Semester 1 Unit 2 Page 2 of Create a check register for the transactions listed by filling in the information. The balance in the account is $ a. You write check # 1034 on 1/2/12 for $54.12 to Publix. b. You withdraw via ATM $50 on 1/4/12. c. You deposit your paycheck of $ on 1/7/12. d. You withdraw via ATM $75 on 1/10/12. There is a $2.95 fee associated with the transaction since the ATM is not affiliated with your bank. e. You pay off your credit card with $ on 1/15/12. f. You write a check for $32.12 to Kroger on 1/31/12 Number Date Description of Transaction Debit (-) Credit (+) Balance $435.99

3 Math of Finance Semester 1 Unit 2 Page 3 of 19 Unit 2.2 Reconciling a Bank Statement How do you make sure that your records are correct? Reconciling a bank statement with your checking book register is a means to make sure that your records are in line with the bank s records. Use your book or the internet to find the following definitions and explain what the terms mean in your own words: Starting balance: Ending balance: Outstanding checks: Outstanding deposits:

4 Math of Finance Semester 1 Unit 2 Page 4 of 19 Below are your check register and your bank statement. Reconcile your check register with your bank statement. Number Date Description of Transaction Debit (-) Credit (+) Balance Previous Balance $ /5/12 Publix $26.76 $ /7/12 Kroger $45.29 $ /15/12 ATM $ $ /17/12 Deposit pay check $ $ /25/12 BestBuys $ $ DATE DESCRIPTION CHECK NUMBER AMOUNT BALANCE 2/1/12 Starting Balance /5/12 Withdrawal /7/12 Withdrawal /15/12 Withdrawal /17/12 Deposit l /29/12 Service Charge /29/12 Ending Balance Solution: The ending balances of the check register and bank statement do not match. The reason is you wrote a check which is outstanding (#105) and you did not include the bank service fee. In order to match the records you have to subtract the service fee ($5.00) from your check register balance and subtract the outstanding check ($103.21) from your ending balance of your bank statement Subtract $5.00 from your check register balance Subtract $ from your bank statement balance Now both statements match

5 Math of Finance Semester 1 Unit 2 Page 5 of Below are your check register and your bank statement. Reconcile both so that they match. Number Date Description of Transaction Debit (-) Credit (+) Balance Previous Balance $ /1/12 Publix $67.34 $ /10/12 Superior Apartments $20.91 $ /15/12 ATM $ $ /17/12 Deposit pay check $ $ /20/12 WalMart $69.34 $ DATE DESCRIPTION CHECK NUMBER AMOUNT BALANCE 3/1/12 Starting Balance /5/12 Withdrawal /13/12 Withdrawal /15/12 Withdrawal /17/12 Deposit l /31/12 Service Charge /31/12 Ending Balance Your check register ending balance is $ Your statement ending balance is $ You have outstanding checks for $25.46 and $ Your service charge is $5.00. Reconcile both statements so that they match.

6 Math of Finance Semester 1 Unit 2 Page 6 of 19 Unit 2.3 Savings Accounts Use your book or the internet to describe following terms in your own words: Savings account Interest Principal Money market account Certificate of deposit (CD) Simple interest

7 Math of Finance Semester 1 Unit 2 Page 7 of 19 You want to deposit $8000 in a certificate of deposit for a period of 2 years. You visit with 4 banks and you are quoted the following rates: 1 3 Wells Fargo: 4 % Bank of America: 4.22% First National: 4 % Peoples Bank: 4.31% 4 8 Wells Fargo: % % 4 4 Bank of America: 4.22% 3 3 First National: 4 % % 8 8 Peoples Bank: 4.31% Therefore, First National offers the highest interest rate with 4.375%. 1. Rank the interest rates from lowest to highest: %, 3.73%, 3 %, 3 %, 3 % You want to deposit $5000 in a certificate of deposit for a period of 2 years. You visit with 4 banks and you are quoted the following rates: 1 7 Wells Fargo: 4 % Bank of America: 4.52% First National: 4 % 2 16 Peoples Bank: 5 4 % 8 Which bank has the highest interest rate?

8 Math of Finance Semester 1 Unit 2 Page 8 of 19 Mitt deposits $1200 in an account that pays 4.5% simple interest. He keeps the money in the account for 3 years without any deposits or withdrawals. How much is in the account after 3 years? Use the simple interest formula, I prt. (where p principal, r interest rate, t time in years) I prt The account generates interest of $162. Add the interest to the principal to arrive at an account balance of $1362 ( = 1362). 3. Mark deposits $7500 in an account that pays 3.25% simple interest. He keeps the money in the account for 2 years without any deposits or withdrawals. How much is in the account after 2 years? 4. Cindy deposits $36700 in an account that pays 7½ % simple interest. She keeps the money in the account for 5 years without any deposits or withdrawals. How much is in the account after 5 years? 5. Chris deposits $ in an account that pays 6¼ % simple interest. He keeps the money in the account for 10 years without any deposits or withdrawals. How much is in the account after 10 years? 6. John deposits $500 in an account that pays 1.25% simple interest. He keeps the money in the account for 1 years without any deposits or withdrawals. How much is in the account after 1 year?

9 Math of Finance Semester 1 Unit 2 Page 9 of 19 You invest $5000 in a simple interest account for 5 years. What interest rate must the account pay so there is $6000 at the end of 5 years? Subtract to find the interest, I The interest is $1000. Use the simple interest formula, I prt : Solve the simple interest formula in terms of r, which is the interest rate: r I pt Plug in the values for I, p, and t to solve 1000 r %. The account must pay 4% annual simple interest You invest $ in a simple interest account for 7 years. What interest rate must the account pay so there is $ at the end of 7 years? 8. You invest $800 in a simple interest account for 2 years. What interest rate must the account pay so there is $850 at the end of 2 years? 9. You want to buy a car for $ You have saved up $ You invest the $15000 in a simple interest account for 3 years. What interest rate must the account pay so there is $18000 at the end of 3 years so that you can buy the car?

10 Math of Finance Semester 1 Unit 2 Page 10 of 19 Unit 2.4 Compound Interest Use your book or the internet to describe following terms in your own words: Compound interest Annual compounding Semiannual compounding Quarterly compounding Daily compounding What is the most common form of compounding?

11 Math of Finance Semester 1 Unit 2 Page 11 of 19 Maria deposits $1000 in a savings account that pays 6% interest, compounded semiannually. What is her balance after 1 year? Convert 6% to a decimal r 6% 0.06 Convert 6 months to years t 6month 0.5 years Use the simple interest formula I prt Substitute and simplify I Add the interest to the principal This new principal of $1030 is used to compute the next six months interest. Use the simple interest formula I prt Substitute and simplify I Add the interest to the principal Maria s balance is $ after one year. Compare that to the balance if you have simple interest for one year. The interest after one year is I prt The balance after one year is $ Maria deposits $3000 in a savings account that pays 4% interest, compounded semiannually. What is her balance after 1 year? 2. Maria deposits $2000 in a savings account that pays 8% interest, compounded semiannually. What is her balance after 3 years? 3. Maria deposits $5000 in a savings account that pays 7% interest, compounded quarterly. What is her balance after 2 years?

12 Math of Finance Semester 1 Unit 2 Page 12 of 19 Unit 2.5 Compound Interest Formula Use your book or the internet to describe following terms in your own words: Annual percentage rate Annual percentage yield The compound interest formula is B r p1 n nt where B ending balance p principal or original balance r interest rate expressed as decimal n number of times interest is compounded annually t number of years You deposit $1650 for three years at 3% interest, compounded daily. A. What is her ending balance? B. What is the interest accumulated? Use the compound interest formula. The values for the variables are p 1650, r 0.03, n 365, t 3.. Substitute the values into the compound interest formula: nt 365(3) r 0.03 B p n 365 Your ending balance is $ The interest accumulated is the ending balance minus the starting balance: $155.38

13 Math of Finance Semester 1 Unit 2 Page 13 of You deposit $3000 in a savings account that pays 4% interest, compounded daily. What is your balance after 3 years? What is the accumulated interest? 2. You deposit $17000 in a savings account that pays 8% interest, compounded daily. What is your balance after 15 years? What is the accumulated interest? 3. Jack deposits $6500 in a savings account that pays 5.75% interest, compounded daily. What is your balance after 2 years? What is the accumulated interest? You deposit $8000 for one year at 3.2% interest, compounded daily. What is the annual percentage yield (APR)? n r Use the APY formula APY 1 1. The values for the variables are r 0.032, n 365. n. Substitute the values into the APY formula: APY % 365 The annual percentage yield is therefore 3.25%. 4. Jack deposits $6500 in a one-year CD that pays 5.75% interest, compounded daily. What is the annual percentage yield? You deposit $2500 in a one-year CD that pays 6.5% interest, compounded daily. What is the annual percentage yield?

14 Math of Finance Semester 1 Unit 2 Page 14 of 19 Unit 2.6 Continuous Compounding Use your book or the internet to describe following terms in your own words: Continuous compounding You deposit $1000 for at 4.3% interest, compounded continuously. What is your ending balance after five years? Use the Continuous Compound Interest Formula: B rt pe where B ending balance p principal e exp onetntial base r int erest rate decimal t number of years B e $ The ending balance is $1, You deposit $3000 in a savings account that pays 4%, compounded continuously. What is your balance after 3 years? What is the accumulated interest? 2. You deposit $5500 in a savings account that pays 2.5%, compounded continuously. What is your balance after 7 years? What is the accumulated interest? 3. You deposit $ in a savings account that pays 6.5%, compounded continuously. What is your balance after 40 years? What is the accumulated interest?

15 Math of Finance Semester 1 Unit 2 Page 15 of 19 Unit 2.7 Future Value of Investments Use your book or the internet to describe following terms in your own words: Future value of a single investment Future value of a periodic deposit investment You deposit $15000 in a mutual fund. You expect an annual return of 9.5%, compounded continuously. What is your ending balance after 40 years? What is the amount of money you earned on the investment? rt B pe where B ending balance p principal e exp onetntial base 2.72 r int erest rate decimal t number of years rt B pe e $670, The ending balance is $670, The amount of money earned is $670, $15,000 = $655, At the age of 25 you make a single deposit of $30,000 into a mutual fund that invests in Dow Jones stocks. Historically stocks in the Dow Jones returned 10% annually. If you expect the same return for the future what will be the amount of money in the mutual fund by the time you are 60 years old?

16 Math of Finance Semester 1 Unit 2 Page 16 of 19 You are 30 years old and open a savings account with Bank of America. You plan to invest $5000 each year until you are at the age of 50. The expected interest is 4.5%, compounded annually. What is the expected account balance when you are 50 years old? Use the formula of a periodic deposit investment r nt P((1 ) 1) B n where B ending balance r n P periodic deposit amount r annual int erest rate decimal (20) 5000((1 ) 1) B 1 $156, The ending balance is $156, n number of times int erest is compounded annually t length of investment in years 1. At the age of 25 you start making yearly periodic payments of $3,000 into a mutual fund. You expect yearly returns of 12%, compounded annually. What is the expected account balance when you are 65? 2. You save up for a car which is $ You start saving $2000 every year and put it into a savings account whith an annual interest rate of 8.5%, compounded yearly. Will you have enough money if you save for 10 years?

17 Math of Finance Semester 1 Unit 2 Page 17 of 19 Unit 2.8 Present Value of Investments Use your book or the internet to describe following terms in your own words: Present value of a single investment Present value of a periodic deposit investment Your parents know that in 6 years you will go to college. They will need $20,000 for the first year s tuition. How much should your parents deposit into an account that yields 5% interest, compounded annually, in order to have that amount? Round your answer to the nearest thousand dollars. Use the formula for the Present Value of a Single Deposit Investment B P where B ending balance r nt (1 ) n p principal or original balance present value r int erest rate decimal n number of times int erest is compounded annually t number of years B P $14, r nt (6) (1 ) (1 ) n 1 Your parents should deposit approximately $15,000 into the account.

18 Math of Finance Semester 1 Unit 2 Page 18 of Bob wants $30,000 at the end of 7 years in order to buy a car. If his bank pays 4.2% interest, compounded annually, how much must he deposit now to reach his goal? 2. Your grandpa wants to open an account for you that he hopes will have $80,000 in it after 20 years. How much must he deposit now into an account that yields 2.75% interest, compounded monthly, so he can reach his goal? 3. Rick needs a $50,000 down payment for a house in 5 years from now. How much must he deposit now into an account that yields 6% interest, compounded quarterly, so he can reach his goal? 4. Sue needs $25,000 for her daughter s wedding in 3 years from now. How much must she deposit now into an account that yields 8% interest, compounded quarterly, so she can reach his goal?

19 Math of Finance Semester 1 Unit 2 Page 19 of 19 Your parents know that in 3 years you will go to college. They will need $15,000 for the first year s tuition. How much should your parents deposit monthly into an account that yields 4% interest, compounded annually, in order to have that amount? Round your answer to the nearest hundred dollars. Use the formula for the Present Value of a Periodic Deposit Investment r B P n where B ending balance r nt (1 ) 1 n P Periodic Investment r int erest rate decimal n number of times you make a deposit per year t number of years r 0.04 B P n 12 $ r nt (3) (1 ) 1 (1 ) 1 n 12 Your parents should deposit approximately $400 monthly into the account in order to have $15,000 in 3 years from now. 1. Bob wants $30,000 at the end of 7 years in order to buy a car. If his bank pays 4.2% interest, compounded annually, how much must he deposit monthly to reach his goal? 2. Your grandpa wants to open an account for you that he hopes will have $80,000 in it after 20 years. How much must he deposit yearly into an account that yields 2.75% interest, compounded annually, so he can reach his goal? 3. Rick needs a $50,000 down payment for a house in 10 years from now. How much must he deposit monthly into an account that yields 6% interest, compounded quarterly, so he can reach his goal?

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