Question

A loan is being repaid with a series of payments at the end of each quarter for 6 years. If the amount of principal in the seventh payment is $210, find the amount of principal in the last 7 payments. Interest is at the rate of 5.3% convertible quarterly. ANSWER = $ ......

Answer 1

The total principal in the last 7 payments is $211.80

Let P24 be the principal amount at the end of the 24th payment. We can use the formula for the future value of an ordinary annuity:

P24 = P7 * (1 + r)^m

Substituting the values:

P24 = $210 * (1 + 0.01325)^17

P24 ≈ $421.80

Calculate the Total Interest Paid in the Last 17 Payments:

The total interest paid in the last 17 payments is the difference between the principal at the end of the 24th payment and the principal in the 7th payment:

Total Interest = P24 - P7

Total Interest = $421.80 - $210

Total Interest = $211.80

Calculate the Principal Amount in the Last 7 Payments:

The principal amount in the last 7 payments is equal to the total interest paid in the last 17 payments:

Principal in last 7 payments = Total Interest

Principal in last 7 payments = $211.80

Therefore, the total principal in the last 7 payments is $211.80