Question

A design studio received a loan of $8,050 at 5.30% compounded semi-annually to purchase a camera. If they settled the loan in 2 years by making quarterly payments, construct the amortization schedule for the loan and answer the following questions:

a. What was the payment size? ___$0.00 Round to the nearest cent
b. What was the size of the interest portion on the first payment? ___$0.00 Round to the nearest cent
c. What was the balance of the loan at end of the first year? ___$0.00 Round to the nearest cent
d. What was the size of the interest portion on the last payment? Round to the nearest cent

Answer 1

a. The payment size is $2,106.16.

b. The size of the interest portion on the first payment is $35.54.

c. The balance of the loan at the end of the first year is $6,970.42.

d. The size of the interest portion on the last payment is $18.46.

Step-by-step explanation:

The payment size can be calculated using the loan amount, interest rate, and the number of payments. In this case, with a loan of $8,050, an interest rate of 5.30%, and quarterly payments over 2 years (8 quarters), the payment size is $2,106.16.

To determine the interest portion on the first payment, the outstanding balance is multiplied by the semi-annual interest rate. For the initial payment, this amounts to $35.54.

The balance at the end of the first year is found by subtracting the principal portion of the payments made in the first year from the initial loan amount.

The balance at the end of the first year is $6,970.42.

The interest portion on the last payment is calculated similarly to the first payment but for the last quarter, resulting in $18.46.

This decreases as more of the principal is paid off with each installment. This amortization schedule provides a clear breakdown of payments, helping track the reduction in the outstanding loan balance over time.