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# Calculating present and future values

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13. The future value of \$200 received today and deposited for three years in an account which pays semiannual interest of 8 percent is ______.
A. \$253.00
B. \$252.00
C. \$158.00
D. \$134.66

14. The future value of \$100 received today and deposited at 6 percent for four years is
A. \$126.
B. \$ 79.
C. \$124.
D. \$116.

15-19. Calculate the present value of the annuity assuming that it is an ordinary annuity.

Case Amount of Annuity Interest Rate Period / Years
A \$14,000 9% 3
B \$17,500 13% 15
C \$975 18% 7
D \$1,127,000 4% 9
E \$10,000 7% 3

20-24. For each of the cases shown below in the table, calculate the present value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years
A \$13,000 10% 5
B \$34,000 17% 25
C \$16,000 6% 18
D \$210,000 15% 15
E \$90,000 20% 9

25-29 For each of the cases shown below in the table, calculate the future value of the cash flow:

Case Single Cash Flow Interest Rate End of Periods / Years
A \$3,000 10% 7
B \$44,000 12% 5
C \$6,000 8% 10
D \$27,000 16% 12
E \$99,000 20% 6

Calculate the above future values in questions 25-29 as semi annual and quarterly compounding.

#### Solution Preview

Please refer attached file for better clarity of formulas.

13.
Present Value of deposit=PV=\$200
Semi annual interest rate=i=8%/2=4%
Number of periods=n=3 years=6 (semi annual periods)
Future Value of deposit=PV*(1+i)^n=200*(1+4%)^6=253.06

14.

Present Value of deposit=PV=\$100
Annual interest rate=i=6%
Number of periods=n=4 years
Future Value of deposit=PV*(1+i)^n=100*(1+6%)^4=126.2477

15-19.

Case A:
Amount of annuity=R=\$14000
Interest rate=i=9%
Periods=n=3 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=14000*(1-1/(1+9%)^3)/9%=\$35,438.13

Case B:
Amount of annuity=R=\$17500
Interest rate=i=13%
Periods=n=15 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=17500*(1-1/(1+13%)^15)/13%=\$113,091.63

Case C:
Amount of annuity=R=\$975
Interest rate=i=18%
Periods=n=7 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=975*(1-1/(1+18%)^7)/18%=\$3,716.24

Case D:
Amount of annuity=R=\$1,127,000
Interest rate=i=4%
Periods=n=9 years
Present Value of annuity=PV=R*(1-1/(1+i)^n)/i=1127000*(1-1/(1+4%)^9)/4%=\$8,379,618.7

Case ...

#### Solution Summary

There are basic 17 problems related to time value of money concepts. Solutions depict the methodology to calculate Present and future values in different cases.

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