Question

A loan of $100,000 is made today. The borrower will make equal repayments of $3418.16 per month with the first payment being exactly one month from today. The interest being charged on this loan is constant (but unknown).

For the following two scenarios, calculate the interest rate being charged on this loan, expressed as a nominal annual rate in percentage:

(a) The loan is fully repaid exactly after 33 monthly repayments, i.e., the loan outstanding immediately after 33 repayments is exactly 0.

(b) The term of the loan is unknown but it is known that the loan outstanding 2 years later equals to $32254.82.

Answer 1

Part A) We are given the following information:

PMT	3418.16
no. of payments n	33
frequency	12
PV	$   1,00,000.00

We need to solve the following equation to arrive at the required rate:

where r is the nominal annual rate.

Following is the amortization schedule and graph

• Opening balance = previous year's closing balance
• Closing balance = Opening balance+Loan-Principal repayment
• Interest = 0.0869992273219028/12 x opening balance
• Principal repayment = PMT - Interest

Part B) We need to solve the following equation to find the interest rate which will lead to loan amount remaining as $32254.82 at the end of 2 years or after 12 x 2 = 24 monthly payments

where r is the nominal annual rate.

Following is the schedule:.