Question

A loan of $100,000 is made today. The borrower will make equal repayments of $818 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. Give your answer as a percentage to 2 decimal places.

(a) The loan is fully repaid exactly after 240 monthly repayments, i.e., the loan outstanding immediately after 240 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 $88068.

please do not round and show working

Answer 1

Sol :

a) Interest rate being charged on loan in senerio 1 is as follows,

Monthly payment = Loan amount x  interest rate x (1+rate)^n/ (1+rate)^n - 1

Using Excel RATE function

Nper = 240 = Number of periods

PMT = 818 = Monthly payments

PV = -100,000 = Loan amount

Monthly rate = 0.64185% Annual interest rate = 0.64175 x 12 = 7.70%

b) Interest rate being charged on loan in senerio 2 is as follows,

Using Excel RATE function

Nper = 24 = Number of periods

PMT = 818 = Monthly payments

PV = -100,000 = Loan amount

FV = 88068 = Loan balance after 2 years

Monthly rate = 0.34% Annual interest rate = 0.34% x 12 = 4.08%

Therefore Interest rate being charged on loan in senerio 1 is 7.70% and Interest rate being charged on loan in senerio 2 is 4.08%