Solve the application problem. Round to the nearest cent.
-How much should be deposited monthly into a sinking fund over 4 years to accumulate $119,000 if the money earns 12% compounded monthly?

Question

Solve the application problem. Round to the nearest cent. 
-How much should be deposited monthly into a sinking fund over 4 years to accumulate $119,000 if the money earns 12% compounded monthly?

Quizplus · Accepted Answer

We can use the formula for present value of an annuity to solve for the monthly payment:
PV = PMT × [1 - (1+r)^(-n)] / r
where PV is the present value (amount we want to accumulate), PMT is the monthly payment, r is the monthly interest rate (12%/12 = 1% = 0.01), and n is the total number of months (4 years × 12 months/year = 48 months).
Plugging in the values, we get:
119,000 = PMT × [1 - (1+0.01)^(-48)] / 0.01
Solving for PMT, we get:
PMT = 119,000 × 0.01 / [1 - (1+0.01)^(-48)]
PMT ≈ $1,943.27
Therefore, the monthly payment should be $1,943.27, which is closest to answer choice A.

Solve the Application Problem