Question

A couple took out a 5-year $30,000 loan to pay for for their wedding. After 5 years, the loan payments they had made to the bank amounted to $38,250. The interest rate on the loan, compounded continuously, is %. If they had taken an 8-year loan instead of a 5-year loan, they would have paid approximately $more. NextReset

Answer 1

Hi there
First find the interest rate using the formula of compounded continuously
The formula is
A=pe^rt
A future value 38250
P present value 30000
R interest rate?
E constant
T time 5 years
We need to solve for r
R=[log (A/p)÷log (e)]÷t
R=((log(38,250÷30,000)÷log(e))÷5)
R=0.049

Now the interest rate is known
Find the balance after 8 years
A=30,000×e^(0.049×8)
A=44,398.13

Hope it helps