Question

A company estimates that it will need $108,000 in 8 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 4.5% compounded monthly, how much should each payment be? The amount of each payment should be $ (Round to the nearest cent.) ***​

Answer 1

We need to calculate the monthly payments required to accumulate $108,000 in 8 years with a 4.5% annual interest rate, compounded monthly.

First, we calculate the total number of compounding periods:

Number of compounding periods = 8 years * 12 months/year = <<8*12=96>>96 months

Next, we calculate the monthly interest rate:

Monthly interest rate = 4.5% / 100% / 12 = 0.045 / 12 = 0.00375

Now, we can use the future value of an ordinary annuity formula to determine the monthly payment amount:

Future value of annuity = Payment * [(1 + Monthly interest rate)^Number of compounding periods - 1] / Monthly interest rate

$108,000 = Payment * [(1 + 0.00375)^96 - 1] / 0.00375

Now, we can solve for the payment amount:

Payment = ($108,000 * 0.00375) / [(1 + 0.00375)^96 - 1]

Payment ≈ $915.21

Therefore, each monthly payment should be approximately $915.21.

Answer 2

So, each monthly payment should be approximately $7,144.07 (rounded to the nearest cent).