Question

# Question 1 Jack took a \$ 5,000 loan, which he repaid in monthly installments over seven...

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?

Please include instalment cost and arrangement fee in the calculations.

Solution

Annual Interest rate on loan is 7%

Ie:-It is calculated by taking interest amount of \$30 paying every installement and the incremental cost and arrangement fee for the loan.

Here,The Jack paying interest on every installement=\$210(7*30)
He paying Management fee on every installement=\$107.8(7*15.4)

In the first and second installment he paying arrangement fee at .5%=7.143(1428.57*.5%)

From the above explanation we can see that jack pays \$ 325 as interest and fee for the loan taken by him.And finding out the real annual interest rate is calculated as follows:-

Total Amount Payable by Jack=\$5325

Total No.of month takes to pay the loan=11 month

Actual amount of loan taken by him=\$5000

Then,325=5000*(11/12)*r/100 here r means rate of interest

325=4583.3*r/100

(325/4583.3)*r/100=.07*r/100

r=.07*100=7%

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