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 $140,000. 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

a.

i = 12%/12 = 1%

Monthly payment = 140000*(A/P,1%,96)

= 140000*0.01*((1 + 0.01)^96)/((1 + 0.01)^96-1)

= 140000*0.01*((1.01)^96)/((1.01)^96-1)

= 140000*0.016252841

= 2275.40

b.

Constant dollar equivalent of last payment = 2275.40*(P/F,0.5%,96)

= 2275.40*(1 + 0.005)^-96

= 2275.40*(1.005)^-96

= 1409.66