Question

PROBLEMS (6.0 Points Each) 1) The following loan is fully amortizing. The loan is for $13,000 at 10% interest to be repaid over three (3) years. Amoliize this loan on a monthly basis. Calculate the interest portion of the fourth {4. payment considering that an additional payment of $2.000 was made with the second payment. (Read this carefully).

Answer 1

Loan Principal outstanding = $13,000

ROI= 10% per annum

Tenure = 3 years

Amortization frequency = Monthly

Prepayment made with the 2nd installment = $2,000

Since, the amortization frequency is monthly, we will have to use the monthly interest rate of 10%/12 = 0.833% for computing the monthly payment.

Using PMT function in Excel or a financial calculator, the monthly payment using the above data comes to $419.47

Here, we will assume that the monthly payment stays constant throughout the tenure of the loan until it is fully amortized. So, even if there has been a prepayment (or additional payment) of $2,000 along with the 2nd payment (installment), the monthly payment will continue to be the same. The impact of this additional payment will be that the principal will reduce by an additional $2,000 at the end of the 2nd payment and as a result, interest portion during the successive payments will be lower compared to the scenario wherein there were no such additional payment made. I will tabulate both these scenarios (with the additional payment and without it) just to clarify the difference in the interest component in the future payments (in this case specifically the 4th payment).

First, lets look at the amortization table for the first 4 months in the absence of the additional payment of $2,000.

Payment No.	Principal outstanding	Interest paid	Principal paid	Additional payment
1st Payment	$13,000.00	$108.33	$311.14	$0.00
2nd Payment	$12,688.86	$105.74	$313.73	$0.00
3rd Payment	$12,375.13	$103.13	$316.35	$0.00
4th Payment	$12,058.78	$100.49	$318.98	$0.00

Since there is no additional payment in this case, the interest portion of the 4th payment is $100.49

Now, lets look at the amortization table for the first 4 months assuming that an additional payment of $2,000 was made along with the 2nd payment.

Payment No.	Principal oustanding	Interest paid	Principal paid	Additional payment
1st Payment	$13,000.00	$108.33	$311.14	$0.00
2nd Payment	$12,688.86	$105.74	$313.73	$2,000.00
3rd Payment	$10,375.13	$86.46	$333.01	$0.00
4th Payment	$10,042.11	$83.68	$335.79	$0.00

Please note that due to the additional payment of $2,000 along with the 2nd payment, the principal outstanding at the beginning of 3rd month was lower by $2,000 compared to the first scenario. This results in lower interest portion in all future payments due to lowering of principal oustanding.

Answer. Hence, the interest portion of the 4th payment is $83.68 in this scenario