Question

A business sets up a sinking fund so they will have a $51,000.00 to pay for a replacement piece of equipment in 11 years when the current equipment will be sold for scrap. If they make deposits at the end of each month for 11 years in the investment that pays 6.3% compounded monthly, what size should each payment be?

Answer 1

The size of each payment should be approximately $328.71.

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 future value (in this case, $51,000), P is the payment size, r is the interest rate per period (in this case, 6.3% per year or 0.063/12 per month), and n is the number of periods (in this case, 11 years or 11*12 months).

Substituting the given values into the formula:

$51,000 = P * [(1+0.063/12)^(11*12) - 1] / (0.063/12)

Simplifying the equation:

P = $51,000 / [(1+0.063/12)^(11*12) - 1] / (0.063/12)

Calculating the value of P:

P ≈ $328.71