Question

Annutiy Due. Reginald is about to lease an apartment for 36 months. The landlord wants him to make the lease payments at the start of the month. The monthly payments are $1,300 per month. The landlord says he will allow Reg to prepay the rent for the entire lease with a discount. The one-time payment due at the beggining of the lease is $39,531.

What is the implied monthly discount rate for the rent? If Reg is earning 1.5% on his savings monthly, should he pay by month or make the one-time payment?

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Answer 1

Monthly Lease Payments = P = $1300

Number of months = n = 36

If the amount is paid upfront, PV = $39531

Let Discount Rate be r

The present value of all the future payments should be equal to the amount paid upfront

=> PV = P + P/(1+r) +....+ P/(1+r)^n-1 =P + P[1- (1+r)^-(n-1)]/r

=> 39351 = 1300 + 1300[1- (1+r)^-35]/r

=> [1- (1+r)^-35]/r = (39351 - 1300)/1300 = 29.27

Using iterative calculation, we get r = 0.01027 = 1.03%

Interest Rate earned in savings account = 1.5%

Since the required return on full lease payment is lower than the return earned in savings account, he should not make the one time payment and should make monthly payments