Question

You are going to sublet one of the rooms in your apartment for the next year for $250 a month. Payments are due at the first of every month, starting tomorrow. If the tenant wanted to pay a lump sum today for the entire year and your discount rate is 3% per year, how much would you receive?

a.

How much does that amount differ if the payment is at the end of each month?

Answer 1

interest rate , r = 3% = 0.03

interest rate per month, i = r/12 = 3/12 = 0.25% = 0.0025

rent per month , x = $250

PERIOD OF RENT , N = 12 MONTHS

lump sum today = x*PVIFA(12 months,0.25%)*(1+i)

PVIFA = present value interest rate factor of annuity = [ (1+i)ⁿ -1]/((1+i)ⁿ *i) = [ (1.0025)¹² -1]/((1.0025)¹² *0.0025) = 11.80725384

lump sum today, L1 = 250*11.80725384*(1.0025) = $2959.19

a)

if payment is at the end of each month

lump sum today, L2 = x*PVIFA = 250*11.80725384 = $2951.81

difference in the 2 amounts = L1 - L2 = 2959.19 - 2951.81 = $7.38