Question

Question 1

Jack took a $ 5,000 loan, which he repaid in monthly installments over seven months. Payments were always made at the end of the month (each payment month was 1/12 part of the year) so that the first repayment was made 4 months after the loan was drawn down. Each equal installment consisted of an installment of the loan amount of $ 5,000 / 7 and an interest component of $ 30 and an account management fee of $ 15.40. In addition, in connection with the first and last repayment installments, an arrangement fee of 0.5% was paid in each of them, which was the amount of the original loan amount.

What was the real annual interest rate on the loan?

Answer 1

Ignoring the management fees and the arrangement fee as they don't contribute to the interest calculation. Hence the equal money installments are =5000/7 + 30 = 744.2857.

The present value of the loan should be equal to 5000. Hence, using the present value formula , we have:

5000 = 744.2857 x (1/(1+r)^4 + 1/(1+r)^5 + ....... + 1/(1+r)^10)

From this we calculate the value of r.

5000/744.2857 = 6.7178 = 1/(1+r)^3 x [1 - 1/(1+r)^7]/r = [1 - 1/(1+r)^7]/r(1+r)^3

r = 0.0059 or 0.59%.

This is the monthly rate of interest. Now we calculate the yearly interest based on this monthly rate.

1 + X = (1+r)^12

X = 7.314%