Question

You are a real estate owner in Bloomington Indiana and you have rented a house to students. You expect to make 6% per year on this leasehold investment. The terms of the lease are for 24 months and the rent is due at the beginning of the month. Your savvy renters are Kelley students and they request that the rent be paid, instead, at the end of the month. How much more will the investor receive as a result of payments at the beginning of the month rather than the student's proposed payments at the end of the month over the entire life of the lease?

Answer 1

Answer:

The present value of the contract is 0.5% higher if the rent is paid at the beginning of the month. That is equal to $11.28 for every $100 of rent.

Explanation:

if the rent is paid at the beginning of the month, the present value of the lease contract will be:

PV = monthly rent x PV annuity due factor

we are not given the monthly rent, but we know the PV annuity due factor for 0.5% and 24 periods = 22.67568

if the rent is paid at the end of the month, the PV = monthly rent x PV ordinary annuity factor

the PV ordinary annuity factor, 0.5%, 24 periods = 22.56287

assuming that the rent is $100 (just to calculate a %), the PV of an annuity due = $2,267.57

the PV of an ordinary annuity = $2,256.29

the difference between them = [($2,267.57 / $2,256.29) - 1] x 100 = 0.5%