Question

In: Economics

A company wants to replay a $117,053 debt making $463 quarterly payment for 21 quarters, then...

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?

Expert Solution

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.

Rahul Sunny answered 7 months ago

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