29) Reginal is about to lease an apartment for the year. The landlord wants him to make the lease payments at the start of the month. The twelve monthly payments are $1,300 per month. The landlord says he will allow Reg to prepay the rent for the entire year with a discount. The one-time annual payment due at the beginning of the lease is $14,778. 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 single annual payment?

The implied monthly discount rate for the rent is 1%

Explanation:

Reg has to pay $1,300 at the beginning of each month or a lumpsum amount of $14778. The discount rate will be such that the present value of 1,300 paid in the year equals 14,778. From present value table, we got the discount rate. Now just compare it with the the rate he can earn oh his deposits

Let the monthly discount rate be x

Since payments are due at the start of month, present value will be calculated as:

14,778 = 1,300 + 1,300*PVAF (x%, 11 periods)

PVAF (x%, 11 periods) = 10.3676

From present value annuity factor table, x = 1%

implied monthly discount rate offered = 1%

If Reg is earning 1.5% per month, he should pay by month, since the discount offered is less than the opportunity cost.

Therefore, The implied monthly discount rate for the rent is 1%