Question

A loan of $28,200 at 4.52% compounded semi-annually is to be repaid with payments at the end of every 6 months. The loan was settled in 3 years.

a) Calculate the size of the periodic payment. Round to the nearest cent
b) Calculate the total interest paid. Round to the nearest cent

Answer 1

The size of the periodic payment for the loan is approximately $4,602.55. The total interest paid for the loan is approximately $3,607.65.

Step-by-step explanation:

To calculate the size of the periodic payment for the loan, we can use the formula for the present value of an annuity:

PV = PMT * [1 - (1 + r/n) ^ (-nt)] / (r/n)

Where PV is the loan amount ($28,200), PMT is the periodic payment, r is the interest rate (4.52%), n is the number of compounding periods per year (2), and t is the number of years (3).

Plugging in the values, we can solve for PMT:

PMT = PV * (r/n) / [1 - (1 + r/n) ^ (-nt)]

Using the calculator, the periodic payment for the loan is approximately $4,602.55.

To calculate the total interest paid, we can use the formula:

Total Interest = (PMT * nt) - PV

Plugging in the values, we can solve for the total interest:

Total Interest = (4,602.55 * 2 * 3) - 28,200

The total interest paid for the loan is approximately $3,607.65.