Question

A business sets up a sinking fund so they will have a $58,000.00 to pay for a replacement piece of equipment in 8 years when the current equipment will be sold for scrap. If they make deposits at the end of each month for 8 years in the investment that pays 7.7% compounded monthly, what size should each payment be?

Answer 1

To calculate the size of each payment, you can use the formula for the future value of an ordinary annuity. Solving the equation, the size of each payment should be approximately $575.27.

Step-by-step explanation:

To calculate the size of each payment, you can use the formula for the future value of an ordinary annuity:

FV = P[((1 + r)^n - 1) / r]

Where:
FV is the future value of the annuity
P is the payment size
r is the interest rate per period
n is the number of periods
In this case, we want to find the payment size, so we rearrange the formula:

P = FV[r / ((1 + r)^n - 1)]

Plug in the given values:
FV = $58,000
r = 7.7% = 0.077 (monthly rate)
n = 8 years * 12 months/year = 96 months

P = $58,000[(0.077) / ((1 + 0.077)^96 - 1)]

Solving this equation, the size of each payment should be approximately $575.27.