Problem Solving

Last year a certain bond with a face value of $5000 yielded 8 percent of its face value in interest. If that interest was approx. 6.5 percent of the bond's selling price, approx. what was the bond's selling price?

A. $4,063
B. $5, 325
C. $5, 351
D. $6,000
E. $6,154

dferm wrote:Last year a certain bond with a face value of $5000 yielded 8 percent of its face value in interest. If that interest was approx. 6.5 percent of the bond's selling price, approx. what was the bond's selling price?

A. $4,063
B. $5, 325
C. $5, 351
D. $6,000
E. $6,154

First, let's figure out the interest:

8% of $5000 = (.08)($5000) = $400

Now we know that $400 = 6.5% of the selling price, so:

400 = (0.065)x

or

400/(.065) = x

Now we can use good ol' long division. Let's multiply top and bottom by 1000 to eliminate the decimals.

400000/65 = 6...

Hey! The first digit is a 6, so let's eliminate (a), (b) and (c). Looking at (d) and (e), we can see it's not going to be exactly 6000, so eliminate (d). Only (e) remains - Done!

Remember - the answer choices are your buddies. Keeping an eye on them can vastly reduce the number of calculations you need to make.

As an aside, we also could have backsolved once we got to:

400 = (0.065)x

We'd eliminate (a) using common sense (we know the answer has to be more than $5000), then try either (c) or (d).

(d) is a better choice, since it's a nice easy number to work with. We'd get:

(.065)(6000) = 390

Well, that's not 400. In fact, it's less than 400. Therefore, we need a bigger number than the one in (d): eliminate (b) and (c) and choose (e).