Question

Annuity due: Reginald is about to lease an apartment for 12 months. The landlord wants him to make the lease payments at the start of the month. The monthly payments are ​$1200 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 beginning of the lease is ​$13714. What is the implied monthly discount rate for the​ rent? If Reg is earning ​1.4% on his savings​ monthly, should he pay by month or make the​ one-time payment?

Answer 1

To calculate the implied monthly discount rate, we can use the formula:

PV = PMT x ((1 - (1 + r)^-n) / r)

Where:

PV = Present value of the one-time payment

PMT = Monthly payment

r = Implied monthly discount rate

n = Number of periods (in months)

Plugging in the given values, we get:

13714 = 1200 x ((1 - (1 + r)^-12) / r)

Solving this equation using a financial calculator or software, we get r = 0.0108 or 1.08%.

Now, to determine whether Reg should pay by month or make the one-time payment, we need to compare the implied monthly discount rate with the interest rate he is earning on his savings. Since Reg is earning 1.4% on his savings monthly, he should choose the option that offers a higher rate of return.

Comparing the two rates, we can see that Reg's savings interest rate of 1.4% is higher than the implied monthly discount rate of 1.08%. Therefore, it would be better for Reg to pay by month rather than making the one-time payment. By paying monthly, he can earn interest on his savings and potentially earn more than the discount offered by the landlord.

Step-by-step explanation: