Question

You are going to purchase your dream home. The owner gives you the option of paying $2,000 per month for the next fifteen years (180 payments) with the first being made one month from now or paying paying $785,000 twenty years from today. If your interest rate is 6% (compounded monthly), which should you take? Remember you will not use 6% as either 6/12= or effective rate.

Answer 1

Answer:

The first option, paying $2,000 per month for the next fifteen years (180 payments) with the first being made one month from now should be taken.

Explanation:

* Calculation of present value of the first option, paying $2,000 per month for the next fifteen years (180 payments) with the first being made one month from now:

  We have: Discounting periods: 180; Discount rate = 6/12 = 0.5%; Monthly payment = 2,000

=> Present value = (2,000/0.5%) * [1 - 1.005^(-180)] = $237,007.3

* Calculation of present value of the second option, paying $785,000 twenty years from today.

  We have: Effective rate = (1+0.5%)^12 - 1 = 6.168%

=> Present value = 785,000/(1+6.168%)^20 = $237,135.7

So, as the present value of option on is lower, it should be taken

Answer 2

Answer: $2000 per month for 15 years.

Explanation:

The first option is an annuity.

We can calculate it's present value by the following formula,

PV of an Annuity = P [ (1 – (1+i)^-n) / i ]

Where,

P is the cash flow per period

i is the rate of interest

n is the frequency of payments

The interest figure we are given needs to be converted to a monthly figure.

= 0.06/12 months

= 0.005

Plugging in the numbers we get

= 2000 ( 1- (1+0.005)^-180) / 0.005

= $237,007.03

This would be the present value of the first option you were given.

The second option would be to calculate the present value of $785,000 in 20 years, today.

That is a simple PV formula which is

= P/(1+r)^n

= 785,000/(1+0.06) ^20

= $244,766.71

Comparing the 2 present values shows that the first option is less than the second and so should be preferable.

Therefore paying $2000 a month for the next 15 years is better and should be taken.

Please do comment or react if you have any questions or concerns or if the answer helped you. This will help others as well. Thank you.