A bank makes a loan of $20,000 to a customer. Interest is to be charged at an ef

ID: 2696189 • Letter: A

Question

A bank makes a loan of $20,000 to a customer. Interest is to be charged at an effective rate of

8% per annum. The loan is to be repaid by monthly payments in arrear over a term of 10 years.

The payments are level for the first 5 years, and then reduced to one-half of their original level

for the remaining 5 years.

i. Calculate the monthly repayment rounded up to the nearest cent.

ii. Calculate the interest paid in the rst monthly payment.

iii. Calculate the interest paid in the nal 12 monthly payments

i. Calculate the total payment (capital plus fee) made by the borrower at the end of 4

years to discharge the loan.

ii. Calculate the annual eective rate of interest the borrower paid on the loan, taking

the fee into consideration.

let annual payment for 1st 5 years = A

i) A*(PVIFA(8%/12,60)+PVIFA(8%/12,120)) = 20000

A =20000/131.74 = 151.81/month for 1st 5 years

and 75.90/month for next 5 years

ii)interest paid in the 1st monthly payment = 133.33

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