Question

3) Kathryn invests $5,403 in a savings

account with a fixed annual interest rate of
9% compounded 4 times per year.
How
long will it take for the account balance to
reach $14,382.05?

Answer 1

t = 11 years

Explanation:

First, convert R as a percent to r as a decimal

r = R/100

r = 9/100

r = 0.09 per year,

Then, solve the equation for t

t = ln(A/P) / n[ln(1 + r/n)]

t = ln(14,382.05/5,403.00) / ( 4 × [ln(1 + 0.09/4)] )

t = ln(14,382.05/5,403.00) / ( 4 × [ln(1 + 0.0225)] )

t = 11 years

Summary:

The time required to get a total amount of $14,382.05 with compoundeded interest on a principal of $5,403.00 at an interest rate of 9% per year and compounded 4 times per year is 11 years.