Question

A company wants to replay a $117,053 debt making $463 quarterly payment for 21 quarters, then one final payment. If the interest is 14 per year, compounded quarter, how much is the final payment?

Answer 1

The future value of the amount after 21 quarters can be calculated as:

Where A is the future value, P is the amount borrowed, r is the rate of interest and n is the number of periods.

Given: P = 117,053

n = 21

r = 14% per annum = 0.14

Since the interest rate is compounded quarterly, the rate of interest will be divided by 4 because there are four quarters in a year and the rate of interest is given per annum.

Putting the values:

So, the total amount to be repaid is $241,062.632.

It is given that $463 are paid in each quarter for 21 quarters. So, the total amount repaid as quarterly installments equals:

Where F.V. is the future value of amount repaid, r is the rate of interest, P is the principal amount and n is the number of periods. Putting the values:

So, $14,505.2817 would be repaid as quarterly installments in 21 quarters.

The final payment will equal the amount left to be repaid which is equal to $241,062.632 - $14,505.2817 = 226,557.35

So, the final payment will be of $226,557.35.