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# Calculating present and future values

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1.
FOR EACH OF THE CASES SHOWN IN THE TABLE BELOW, CALCULATE THE FUTURE VALUE OF THE SINGLE CASH FLOW DEPOSITED TODAY THAT WILL BE AVAILABLE AT THE END OF THE DEPOSIT PERIOD IF THE INTEREST IS COMPOUNDED ANNUALLY, SEMI ANNUALLY AND QUARTERLY AT THE RATE SPECIFIED OVER THE GIVEN PERIOD.

CASE SINGLE CASH FLOW INTEREST RATE DEPOSIT PERIOD (YEARS) SEMI ANNUAL ANNUAL QUARTERLY
A \$750 8% 10
B \$3,250 12% 5
C \$9,500 16% 2
D \$10,000 20% 4

2. WHAT SINGLE INVESTMENT MADE TODAY, EARNING 14% ANNUAL INTEREST WILL BE WORTH \$9,000 AT THE END OF 7 YEARS?

3.WHAT IS THE PRESENT VALUE OF \$7,000 TO BE RECEIVED AT THE END OF 5 YEARS IF THE DISCOUNT RATE IS 11%?

4.WHAT IS THE MOST YOU WOULD PAY TODAY FOR A PROMISE TO REPAY YOU \$3,000 AT THE END OF 5 YEARS IF YOUR OPPORTUNITY COST IS 9%?

#### Solution Preview

Please refer attached file for better clarity of formulas in MS Excel.

Case A
Annual Compounding
PV= \$750
Rate=i=8%
Number of periods=n=10
FV=?
FV=PV*(1+i)^n=\$1,619
or Use FV function in MS Excel as under
FV= (\$1,619)

Semi annual Compounding
PV= \$750
Rate=i=8%/2=4% per semi annual
Number of periods=n=10*2 20 Semi annuals
FV= ?
FV=PV*(1+i)^n=\$1,643
or Use FV function in MS Excel as under
FV=(\$1,643)

Quarterly Compounding
PV= \$750
Rate=i=8%/4=2% per semi annual
Number of periods=n=10*4 40 Quarters
FV= ?
FV=PV*(1+i)^n=\$1,656
or Use FV function in MS Excel as under
FV=(\$1,656)

Case B
Annual Compounding
PV= \$3,250
Rate=i=12%
Number of periods=n=5
FV=?
FV=PV*(1+i)^n=\$5,728
or Use FV function in MS Excel as under
FV= (\$5,728)

Semi annual ...

#### Solution Summary

Solutions to given problems explains the methodology to find present/future values in the given cases.

\$2.19

## Present & Future Interest Rates - Future value calculation Without referring to tables or to the preprogrammed function on your financial calculator ...

Future value calculation Without referring to tables or to the preprogrammed function on your financial calculator, use the basic formula for future value along with the given interest rate, i, and the number of periods, n, to calculate the future value interest factor in each of the cases shown in the following table.
Compare the calculated value to the value in Appendix Table A-1.

LG2
Case Interest rate, i Number of periods, n
A 12% 2
B 6% 3
C 9% 2
D 3% 4

Present value calculation Without referring to tables or to the preprogrammed function on your financial calculator, use the basic formula for present value, along with the given opportunity cost, i, and the number of periods, n, to calculate the present value interest factor in each of the cases shown in the accompanying table. Compare the calculated value to the table value.

LG2

Case cost Opportunity Cost, i Number of periods, n
A 2% 4
B 10% 2
C 5% 3
D 13% 2

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