Question

3. Determine the value at the end of eight years of a $3,200 investment today that pays a nominal annual interest rate of 18%, compounded: a) Annually b) Semiannually c) Quarterly d) Monthly

Answer 1

Solution:

Present value or principal = 3200

Nominal annual interest rate = 18%

Time = 8 years

A) Value at end of 8 years if compounded Annually:

Future Value or final amount = Principal * (1+Per period interest rate)^(Total number of periods)

Compounded period = Annual

Per period interest rate = 18%/1= 18%.

Total number of periods = 8 * 1 = 8.

Future Value or final amount = 3200 * (1+ 0.18)^(8) = 12028.349.

B) Value at end of 8 years if compounded SemiAnnually:

Future Value or final amount = Principal * (1+Per period interest rate)^(Total number of periods)

Compounded period = SemiAnnual

Per period interest rate = 18%/2= 9%.

Total number of periods = 8 * 2 = 16.

Future Value or final amount = 3200 * (1+ 0.09)^(16) = 12704.979.

C) Value at end of 8 years if compounded Quarterly:

Future Value or final amount = Principal * (1+Per period interest rate)^(Total number of periods)

Compounded period = Quarterly

Per period interest rate = 18%/4= 4.5%.

Total number of periods = 8 * 4 = 32.

Future Value or final amount = 3200 * (1+ 0.045)^(32) = 13087.939.

D) Value at end of 8 years if compounded monthly:

Future Value or final amount = Principal * (1+Per period interest rate)^(Total number of periods)

Compounded period = Monthly

Per period interest rate = 18%/12= 1.5%.

Total number of periods = 8 * 12 = 96.

Future Value or final amount = 3200 * (1+ 0.015)^(96) = 13362.571.