# Casio Financial Consultant A Supplementary Reader - Part 2

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1 Casio Financial Consultant A Supplementary Reader - Part 2 An Electronic Publication By

2 Contents i CASIO Financial Consultant: A Supplementary Reader - Part 2 CONTENTS Page Introduction ii Compound Interest with 1 Doing Amortization with AMRT 4 FC-2V & FC-1V Comparison Chart

4 Compound Interest with 1 Compound Interest with The enhanced display screen and apparent interactivity of the FC 1V/2V actually makes calculation such as compound interest calculation much easier. In our discussion we calculate partial month using compound interest, and we use j (compounded m times a year) to represent the nominal interest rates. m Example 1 >> Enter mode and set partial month calculation to CI. SETUP Enter mode by tapping on, then tap on. If [dn:ci] is displayed, let it be. Otherwise, scroll down and set it to CI. 1 So we have set partial month calculation as [dn:ci]. Example 2 >> Find the compound interest on \$1, for 2 years at 12% compounded semi-annually, or j 2= 12%. In mode, n is the number of compound periods, P/Y is the number of annual payment, while C/Y is the number of annual compounding. Check page E-45 of the User Guide. As interest is compounded twice a year, the number of compound periods is n = 2x2 = 4. Also, interest is paid twice a year, so we have P/Y = 2. Lastly, C/Y is the number of annual compounding, so C/Y is 2. Enter mode and make sure the calculator displays [Set:End]. Scroll down, enter 2 for [n], 12 for [I%], (-)1 for [PV], for [PMT], 1 for [P/Y] and 2 for [C/Y] ( ) Screenshot from Casio TVM Scroll up to select [FV] and solve it. Output: FV = So the future value (sum of principal and accumulated interest) is approximately \$ Obviously the compound interest is \$ \$1 = \$

5 Compound Interest with 2 Example 3 >> Find the monthly installment of a 25-year, \$1, mortgage loan at interest of 6.25% compounded monthly. In this example, n = 25x12 = 3, I% = 6.25, PV = 1,, P/Y (installment paid monthly) = C/Y = 12. Enter mode. The calculator should display [Set:End] since payment is made at the end of each period. Enter 25x12 for [n], 6.25 for [I%], (-)1, for [PV], 12 for [P/Y] and 12 for [C/Y] ( ) 1 Screenshot from Casio TVM Scroll up to select [PMT] and solve it. Output: PMT = Therefore the monthly installment of the mortgage loan is about \$ Suppose the mortgage loan above is calculated based on daily interest, so to find the monthly repayment, we set [C/Y] as 365 and then solve for [PMT] again. The mode also enables user to find other parameters such as interest rate. Example 4 >> The earning per share of common stock of a company increased from \$4.85 to \$9.12 for the last 5 years. Find the compounded annual rate of increase. In this example, n = 5, PV = (payment made earlier), FV = 9.12, while P/Y = C/Y = 1. All other parameters =. Enter mode, ensure that [Set:End] is displayed. Enter 5 for [n], for [PV], 9.12 for [FV] and 1 for both [P/Y] and [C/Y]. 5 ( ) Screenshot from Casio TVM

6 Compound Interest with 3 Now scroll up to select [I%] and solve it. Output: I% = Therefore the compounded annual increase rate of this stock for the last 5 years is about 13.46%. The previous example shows that when sufficient information is provided, we could calculate for most parameters available in mode. The next example is simple annuity calculation made possible with the mode of FC-1V/FC-2V. Example 5 >> My friend JT was repaying a debt with payments of \$25 a month. He misses his payments for November, December, January and February. What payment will be required in March to put him back on schedule, if interest is at j 12 = 14.4%? In this example, Set = End, n = 5 (months), I% = 14.4, PMT = 25, P/Y = C/Y = 12. Other parameters =. Once entered mode, make sure that [Set:End] is shown. Enter 5 for [n], 14.4 for [I%], for [PV], 25 for [PMT], 12 for both [P/Y] and [C/Y] Scroll up to select [FV] and solve it. Output: FV = Hence JT needs to settle \$ in March to get back on the loan repayment schedule. For Understanding >> A company estimates that a machine will need to be replaced 1 years from now at a cost of \$35,. How much must be set aside each year to provide that money if the company s savings earn interest at j 2 = 8%? Answer: \$

7 Doing Amortization with AMRT 4 Doing Amortization with AMRT The AMRT mode of 1V/2V allows user to perform amortization, which shares many parameters/variables with the mode. In examples that follow we shall be able to see the advantage of such sharing. Note that some amortization problems are actually simple annuity problems which we can solve using the mode (refer to Example 5 of Compound Interest with ). This first example finds the outstanding balance of a loan after certain numbers of payment are made. Example 1 >> A loan of \$5, is to be amortized with equal monthly payment over 2 years at j 12= 7%. Find the outstanding principal (balance) after 8 months. Check page E-55 of the user guide for definitions of PM1, PM2, BAL, INT, PRN, INT and PRN. For this example, n = 2x12 = 24, I% = 7, PV = -5,, P/Y = = C/Y = 12. Other parameters =. As we need to know the monthly payment of the loan, so we begin at mode. When monthly payment is found we proceed to AMRT mode for other calculations. Enter mode, make sure calculator displays [Set:End]. Scroll down, enter 24 for [n], 7 for [I%], (-)5 for [PV], for [FV], 12 for [P/Y] and [C/Y] ( ) Now scroll up to select [PMT] and solve it. Output: PMT = So the monthly payment for the loan is about \$ Now find the outstanding principal. Enter AMRT mode, scroll down to enter 1 for [PM1] and 8 for [PM2]. AMRT 1 8 Scroll down further to select [BAL:Solve] and solve it. Output: BAL = Therefore the outstanding balance after 8 payments is approximately \$

8 Doing Amortization with AMRT 5 In this last example we could have entered values other than 1 to PM1 and still get the same result, as long as the values entered are integer 1. However, in most circumstances we should always let PM1 < PM2 whenever possible (see page E-57 of User Guide.) Example 2 >> Referring to Example 1, find the interest portion and the principal portion of the 9 th payment. If you are doing this immediately after Example 1, then all relevant values are still intact and you can continue; otherwise you should enter those values again. Enter AMRT mode, scroll down to enter 9 for [PM1], make sure [PM2] is not =. AMRT 9 Scroll down further to select [INT:Solve] and solve it. Output: INT = Therefore the interest portion of this 9 th payment is about \$19.9. Return to AMRT, and then scroll to select [PRN:Solve] and solve it. ESC Output: PRN = The calculator indicates that the principal portion of 9 th payment is about \$ Example 3 >> Lucas borrows \$35, at j = 3 12 % to buy a car. The loan should be repaid with monthly installment over three years. Find the total interest paid in the 12 payments of the second year. Again we begin at mode to find the monthly payment of the loan. Enter mode and make sure calculator displays [Set:End]. Then scroll down and enter 36 for [n], 3 for [I%], (-)35 for [PV], for [FV], 12 for [P/Y] and [C/Y] ( ) Screenshot from Casio TVM

9 Doing Amortization with AMRT 6 Now scroll up to select [PMT] and solve it. Output: PMT = The monthly payment is about \$ Next, to find the total interest paid in the second year. Enter AMRT mode and scroll down to enter 13 for [PM1] and 24 for [PM2]. AMRT Screenshot from Casio TVM Scroll down further to select [ INT:Solve] and solve it. Output: INT = The interest paid in the second year is \$ Note that we entered 13, not 12, for PM1. This is due to the definition of PM1 (see page E-56 of User Guide.) Interest rate of mortgage tends to change accordingly and this can affect the total repayment amount, as well as the length of time needed to repay the debt. Example 4 >> QED Finance issues mortgages where payments are determined by interest rate that prevails on the day the loan is made. The monthly payments do not change although the interest rate varies according to market forces. However, the duration required to repay the loan will change accordingly as a result of this. Suppose a person takes out a 2-year, \$7, mortgage at j = 9 12 %. After exactly 2 years interest rates change. Find the duration of the loan and the final smaller payment if the new interest rate stays fixed at j = 1 12 %. First we should find the monthly payment of the loan. Enter mode, make sure calculator displays [Set:End]. Then scroll down and enter 24 for [n], 9 for [I%], (-)7 for [PV], for [FV], 12 for [P/Y] and [C/Y] ( )

10 Doing Amortization with AMRT 7 Now scroll up to select [PMT] and solve it. Output: PMT = The monthly repayment amount is \$ Next, find the outstanding principal after 2 years. Enter AMRT mode and scroll down to enter 1 for [PM1] and 24 for [PM2]. Then, scroll to select [BAL:Solve] and solve it. AMRT Output: BAL = The new loan duration will be calculated using this new outstanding balance where the monthly payment remains at \$ but the interest rate is now at j 12 = 1%. To find the changed loan duration we return to mode, enter the new outstanding balance as PV and enter 1 for [I%]. Note that the new outstanding balance is now stored in the Answer Memory. 1 Ans Once these values are entered, scroll up to select [n] and solve it. Output: n = Thus there are 265 more payment of \$ plus a final smaller payment. In other words the new loan duration is 266 months, or total is = 29 months. Finally, we find the future value of the repayment with loan duration of 266 months; the difference between this future value and monthly payment is the final payment. While in mode, enter 266 for [n], and scroll down to select [FV] and solve it Output: FV = Now calculate PMT + FV (FV is negative) at COMP mode. COMP SHIFT CTLG (VARS) + SHIFT CTLG Output: PMT + FV = Therefore the final, smaller payment is \$

11 Doing Amortization with AMRT 8 Often borrower would want to re-finance long term loan. Using and AMRT in combination, we can easily compare the cost of re-financing with the savings due to decide whether the re-financing exercise would be profitable. Example 5 >> A borrower has an \$8, loan with QED Finance which is to be repaid over 4 years at j 12 = 18%. In case of early repayment, the borrower is to pay a penalty of 3 months payments. Right after the 2 th payment, the borrower determines that his banker would lend him the money at j = %. Should he refinance? ( ) First let s find the monthly payment of the loan. Enter mode, make sure calculator displays [Set:End]. Then scroll down and enter 48 for [n], 18 for [I%], (-)8 for [PV], for [FV], 12 for [P/Y] and [C/Y]. Scroll up to select [PMT] and solve it. Output: PMT = So the monthly payment is about \$235 and the outstanding principal after 2 payments would be about \$534.78, as calculated below. Enter AMRT mode and scroll down to enter 1 for [PM1] and 2 for [PM2]. Then, scroll to select [BAL:Solve] and solve it. AMRT 1 2 Output: BAL = Thus the total to be refinanced is (235) = \$ Now we can obtain the new monthly payment at mode for comparison. Enter mode, enter 28 (less 2 months) for [n], 13.5 for [I%], (-) for [PV]. Other parameters values are retained ( ) Screenshot from Casio TVM

12 Doing Amortization with AMRT 9 With [PMT] now selected, press to solve it. Output: PMT = Thus the new monthly payment is \$252.91, which exceeds the original monthly payment of \$235. Clearly the re-financing exercise is not profitable.

13 FC-2V/FC-1V Comparison Chart Calculator Functions FC-2V FC-1V Scientific Calculation Yes Yes 1- & 2- Variable Statistics Yes Yes Statistical Regression Yes Yes Simple Interest Yes Yes Compound Interest Yes Yes Cash Flow (IRR, NPV, PBP, NFV) Yes Yes Amortization Yes Yes Interest Rate Conversion Yes Yes Cost & Margin Calculation Yes Yes Days and Date Calculation Yes Yes Depreciation Yes - Bonds Yes - Breakeven Point Yes - Key Applications Business and Finance Studies Banking and Banking Studies Insurance and Financial Planning Investment Appraisal Stock Market and Bonds Business and Financial Investment Product Features Expression Entry Method Algebraic Screen Display 4 Lines x 16 Characters Memory (plus Ans Memory) 8 Programmable? No Settings and Functions Short Cut Keys Yes, 2 Function Catalog Yes Batteries Solar Cell & LR44 1 x AAA-Size Dimension (mm) 12.2 x 8 x x 8 x 161 Weight 15g 11g Compiled for Marco Corporation. June 27

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