A bookstore offers you the following deal: you pay $31 today (in January) and you get...

A bookstore offers you the following deal: you pay $31 today (in January) and you get 5%

off the price of everything you purchase in December (for simplicity assume exactly 12

months from now). If your savings account earns 4.50% APR (compounded monthly), how

much do you have to buy in December to just break even on the offer?

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Expert Solution

You pay today in January (PV) = $31

Interest rate (r)= 4.50% p.a. compounded monthly

Time (t)= 12 months

FV = PV * (1+r/12)¹²

FV= 31*(1+4.50%/12)¹²

FV = $32.4235

Since there is 5% off the price you purchase in December. Let us assume you buy ‘X’ in December and in order to break even on the offer:

X*(1-5%) = 32.4235

X= $34.13

You have to buy $34.13 in December to break even on the offer.

jeff jeffy answered 2 years ago

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