Question

You can choose between the following rent payments; you are the tenant in the apartment:

a.        A lump sum cash payment of $12,500;

b.        12 monthly payments of $1,100 each, the first occurring at the end of the month

Which rental payment scheme would you choose if the interest rate was 5% APR with monthly compounding? What is the difference between the two options in today's dollars?

Select one:

a. A is better, difference =486.22

b. B is better, difference =486.22

c. B is better, difference =349.34

d. A is better, difference = $349.34

Answer 1

Present value of option A =$12,500

Present value of option B:

Monthly interest rate = 5%/12 = 0.4166667%

Present value = 1,100*PVAF(0.4166667%, 12 periods)

= 1,100*11.681222

=$12,849.34

Hence, B is better by $349.34

I.e. c is the right answer

Answer 2

To determine which rental payment scheme is better, we need to compare the present value of the two options. The option with the lower present value would be preferred.

Option A: Lump sum cash payment of $12,500. Option B: 12 monthly payments of $1,100 each, the first occurring at the end of the month.

To calculate the present value of Option A, we can directly use the lump sum amount of $12,500.

To calculate the present value of Option B, we need to discount each monthly payment back to its present value using the interest rate of 5% APR with monthly compounding.

Let's calculate the present value of Option B:

PV = PMT * [1 - (1 + r)^(-n)] / r

Where: PV = Present value PMT = Monthly payment r = Monthly interest rate n = Number of payments

PV = $1,100 * [1 - (1 + 0.05/12)^(-12)] / (0.05/12)

Now, let's calculate the present values of Option A and Option B using the given formulas.

Present value of Option A: $12,500

Present value of Option B: $1,100 * [1 - (1 + 0.05/12)^(-12)] / (0.05/12) ≈ $12,150.66

The present value of Option A is $12,500, and the present value of Option B is approximately $12,150.66.

To determine the difference between the two options in today's dollars, we subtract the present value of Option B from the present value of Option A:

Difference = Present value of Option A - Present value of Option B Difference = $12,500 - $12,150.66 ≈ $349.34

Therefore, the correct answer is: d. A is better, difference = $349.34