Question

A young couple has made a nonrefundable deposit of the first month's rent (equal to $1000) on a one-year apartment lease. The next day they find another apartment that they like just as well, but its monthly rent is only $900. They plan to be in the apartment for a year. Should they switch to the new apartment? Assume an (annual) interest rate of 12%.

Answer 1

Let us find the present value of all future rent payments

Interest Rate = 12%

Apartment 1
Non Refundable Deposit = $1000
Monthly Rent = P = $1000
Number of months = n = 12
Interest Rate = r = 0.12/12 = 0.01
PV = ΣP/(1+r)n = 1000/(1+0.01) + 1000/(1+0.01)² +....+ 1000/(1+0.01)ⁿ = 1000[1- (1+0.01)^-12]/0.01 = $11255.07

Apartment 2
Non Refundable Deposit = $0
Monthly Rent = P = $900
Number of months = n = 12
Interest Rate = r = 0.12/12 = 0.01
PV = ΣP/(1+r)n = 900/(1+0.01) + 900/(1+0.01)² +....+ 900/(1+0.01)ⁿ = 900[1- (1+0.01)^-12]/0.01 = $10129.57

Refundable deposit in Apartment 1 = 1000

Savings if opted for Apartment 2 = 11255.07 - 10129.57 - 1000 = 125.5

Hence, they should switch to the new apartment