# Calculating present and future values

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

Answer is A. $253

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

Answer is A. $126

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.