Question

A business sets up a sinking fund so they will have a $75,000.00 to pay for a replacement piece of equipment in 12 years when the current equipment will be sold for scrap. If they make deposits at the end of each month for 12 years in the investment that pays 6.1% compounded monthly, what size should each payment be?

Answer 1

To find the size of each monthly payment for the sinking fund, we can use the formula for the future value of an ordinary annuity. Substituting the values into the formula, we find that each monthly payment should be approximately $364.43.

Step-by-step explanation:

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

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

Where:

• FV is the desired future value ($75,000)
• P is the monthly payment we want to find
• r is the monthly interest rate (6.1% / 12)
• n is the number of months (12 years * 12)

Substituting the values into the formula, we have:

$75,000 = P * ((1+0.061/12)^(12*12) - 1) / (0.061/12)

Solving for P, we find that each monthly payment should be approximately $364.43.