Question

A person decides to get a loan from the bank (today) to finance buying a piece of land. The
borrowed amount is equal to $120,000. The arrangements with the bank state that the loan
will be paid off in 96 equal monthly payments, based on an annual market/combined rate of
12% compounded monthly.
a) Calculate the monthly payment considering the given market/combined rate. (10 points)
b) If the monthly inflation rate is estimated to be 0.5%, calculate the value of the last payment
(96th payment) in constant-worth dollars (i.e. when excluding inflation). (15 points)

Answer 1

Solution :

a) Borrowed Amount (P) = $120,000

Term of loan (N) = 96 months

Market rate (r) = 12% per annum or 1% per month

Formula for monthly payments (EMI) –

P = EMI/ (1+r) + EMI/ (1+r)² +………….+ EMI / (1+r)^N

=>   EMI = [P * r * (1+r)^N ] / [(1+r)^N – 1]

=>   EMI = [120000 * 0.01 * (1+0.01)⁹⁶ ] / [(1+0.01)⁹⁶ – 1]

=> Monthly Payment (EMI) = $1,950.34

b) Monthly inflation rate (i) = 0.5% ( or 0.005)

Last month (96^th ) payment = $1,950.34

So, value of last payment in constant worth dollars = $1,950.34 / (1+i)⁹⁶ = $1,950.34 / (1+0.005)⁹⁶

=> Value of last payment in constant worth dollars = $1.208.28