Question

A company wants to repay a $103,112 debt making $1,335 quarterly payment for 30 quarters, then one final payment. If the interest is 2% per year, compounded quarterly. how much is the final payment (future value at the end of the horizon?

Answer 1

The final payment at the end of the horizon is $637,908.80.

Step-by-step explanation:

To calculate the final payment, we can use the formula for the future value of an annuity:

Future Value = Payment * ((1 + interest rate) ^n - 1) / interest rate

In this case, the payment is $1,335, the interest rate is 2% per year compounded quarterly, and the number of quarters is 30. Using these values in the formula, we can calculate the future value:

Final Payment = $1,335 * ((1 + 0.02/4) ^ (30*4) - 1) / (0.02/4)

Simplifying the equation:

Final Payment = $1,335 * ((1.005) ^ (120) - 1) / 0.005

Calculating this expression gives us the final payment:

Final Payment = $1,335 * (1.348719 - 1) / 0.005 = $637,908.80