Question

Steve Fowler borrowed $97,230 on March 1, 2015. This amount plus accrued interest at 10% compounded semiannually is to be repaid March 1, 2025. To retire this debt, Steve plans to contribute to a debt retirement fund five equal amounts starting on March 1, 2020, and for the next 4 years. The fund is expected to earn 9% per annum.

How much must be contributed each year by Steve Fowler to provide a fund sufficient to retire the debt on March 1, 2025? (Round factor values to 5 decimal places, e.g. 1.25124 and final answer to 0 decimal places, e.g. 458,583.) Annual contribution to debt retirement fund

Annual contribution to debt retirement fund $______

Answer 1

Solution:

Firstly we need to compute the amount to be repaid for loan on march 1, 2025.

Future value = $97,230(1+0.10/2)²⁰ = $257,980.14

Now, since Steve wants to discharge this amount at march1, 2025 then his accumulated amount in 5 year (from march1,2020 to march1,2025) in the debt retirement fund must be equal to the above amount.

It's mean this is also the future value of annual contribution toward debt retirement fund.

therefore, Future value of annuity = Annual contribution ({(1+i)ⁿ - 1 } / i) * (1 + i)

$257,980.14 = Annual contribution ( {(1.09)⁵ - 1 } /0.09) * (1.09)

Thus, Annual contribution = $257,980.14 / 6.5233346= $39,547 (Rounded off)