A company estimates that it will need 144000 in 16 years to replace a computer. If it establishes a sinking fund by making fixed monthly payments into an account paying 3.6% compounded​ monthly, how much should each payment​ be?

Answer 1

To find the monthly payments needed for the sinking fund, we need to use the future value formula for an ordinary annuity.

The future value (FV) of an ordinary annuity is given by the formula:

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

Where P is the monthly payment, r is the monthly interest rate, and n is the number of payments.

In this case, the future value (FV) is given as $144,000, the monthly interest rate (r) is 3.6% or 0.036, and the number of payments (n) is 16 years * 12 months = 192 months.

Substituting these values into the formula, we have:

$144,000 = P * (((1 + 0.036)^192) - 1) / 0.036

Now we can solve for P.

$144,000 * 0.036 = P * (((1 + 0.036)^192) - 1)

$5,184 = P * (((1.036)^192) - 1)

Dividing both sides by (((1.036)^192) - 1), we get:

P = $5,184 / (((1.036)^192) - 1)

Calculating this value, we find:

P ≈ $517.60

Therefore, each monthly payment should be approximately $517.60.