Question

Decision making: Plan 1: An item can be purchased for $625 cash. Plan 2: The store advertises that the same item can be purchased by paying $100 down, $275 at the end of 9 month(s) and $300 at the end of 1 year(s).

1) If money is worth 11.49% simple interest to the buyer, does Plan 1 or Plan 2 offer the better deal? (Enter either 1 or 2.)

2) By how much is it a better deal?

Answer 1

Given data:

Plan 1

Purchase price = $625

Plan 2

Down payment = $100

First payment = $275(9 months)

Second payment = $300(12 months or 1 year)

Simple interest = 11.49% per year (Assumed) = 11.49/12 = 0.96% per month

We have

Simple interest formula

F = P(1+in) or P = F / (1+in)

Where F = Future worth, P = Present worth, I = interest rate & n = tenure or time period

Solution:

1.

Using the above formula let us find out the present worth of Plan 2 in order to compare it with Plan 1 in other words what is the worth of plan 2 today. In order to do so we need to find out the present value of the two payments coming in 9^th month and 12^th month.

Present worth (P1) = 275 / (1+0.0096*9) = 253.13 = $253

Present worth (P2) = 300 / (1+0.0096*12) = 269.05 = $269

Present worth = 100 + 253 + 269 = $622

Plan 2 is a better deal.

2. Therefore, Plan 2 is economical than Plan 1 by $3 (by how much it is better).