You currently have $5,400. First United Bank will pay you an annual interest rate of 8.9, while Second National Bank will pay you an annual interest rate of 10. How many fewer years must you wait for your account value to grow to $13,900 at Second National Bank?

a. 1.06 years

b. 1.08 years

c. 1.40 years

d. 1.17 years

e. 1.32 years

The correct answer is D.

Explanation:

Giving the following information:

You currently have $5,400. First United Bank will pay you an annual interest rate of 8.9, while Second National Bank will pay you an annual interest rate of 10.

We need to calculate the amount of time of each bank using the following formula:

n=[ln (FV/PV) ]/ln (1+r)

First bank:

n = ln (13,900/5,400) / ln (1.089) = 11.089 years

0.089*365 = 32 days

n = 11 years and 32 days

Second bank:

n = ln (13,900/5,400) / ln (1.10) = 9.92 years

0.92*365 = 336 days

n = 9 years and 336 days

Difference = 11.089 - 9.92 = 1.17 years