You just bought expensive car stereo for $2,400 online at Mississippi Best store

Question

You just bought expensive car stereo for $2,400 online at Mississippi Best store. The store offered you a choice – X% discount if you pay right now or you can pay within six months. You can borrow money at your bank at 8.40% per annum compounded monthly.

What is the lowest X% for which you will pay the store right now?

You should answer as the percentage. For example if the answer is 14.5%, then enter 14.5 as the answer.

(Hint: Refer to the Cash Discount Practice Problem. Assume 360 days in a year. Monthly bank interest rate to be paid is annual rate/12)

Explanation / Answer

First we will find the present value of $2,400 if we pay within six month using interest rate of 8.40% per annum compounded monthly.

We know , PV = FV / (1 + i)n

where , i = interest rate per compounding period = 0.084/12 = 0.007 ;

n = total number of compounding period = 6.

PV =$2,400 / (1 + 0.007)6 = $2,400 * 0.95901 = $2,301.62

Minimum amount of desired discount if we pay right now = $2,400 - $2,301.62 = $98.38

lowest X% (cash discount) = ($98.38 / $2,400 ) *100 = 4.10 % or 4.10

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