Interest Rate Word Problem

[jk2010]

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

A - $4063
B - $5323
C - $5351
D - $6000
E - $6154

E

I am sure I am missing a simple step here. Thanks for the help!

[shovan85]

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

A - $4063
B - $5323
C - $5351
D - $6000
E - $6154

E

I am sure I am missing a simple step here. Thanks for the help!

Last year a certain bond with a face value of $5000 yielded 8% of its value in interest.
So the yielded interest was = 8% of 5000 = 400

This $400 is 6.5% of selling price.

Thus the 100% is the selling price = (400/6.5) * 100 = 6153.8

Approximately 6154

[GMATGuruNY]

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

A - $4063
B - $5323
C - $5351
D - $6000
E - $6154

E

I am sure I am missing a simple step here. Thanks for the help!

Interest = .08*5000 = 400.

Now let's find 6.5% of the answer choices -- which represent the selling price -- to see which answer choice yields 400.

Let's start with D, since it's a round number:
.065*6000 = 390.
Not quite 400. The selling price has to be just a bit larger.

The correct answer is E.

[melguy]

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

A - $4063
B - $5323
C - $5351
D - $6000
E - $6154

E

I am sure I am missing a simple step here. Thanks for the help!

Interest = .08*5000 = 400.

Now let's find 6.5% of the answer choices -- which represent the selling price -- to see which answer choice yields 400.

Let's start with D, since it's a round number:
.065*6000 = 390.
Not quite 400. The selling price has to be just a bit larger.

The correct answer is E.

Thanks GMATGuru.
Since this question has so many approximately I thought 390 is "approximately" 400. So I picked D instead of E.

[smkhan]

Since 8% of 5000 is equal to 6.5% of some number "x", the number x must be more than 5000. Using answer choice D, 400/6000 *100=6.666% so the denom must be more than 6000. Only choice left is E.

[Needgmat]

Interest = .08*5000 = 400.

Now let's find 6.5% of the answer choices -- which represent the selling price -- to see which answer choice yields 400.

Let's start with D, since it's a round number:
.065*6000 = 390.
Not quite 400. The selling price has to be just a bit larger

The correct answer is E.

Hi GMATGuruNY ,

Can you please explain with the algebraic approach?

Many thanks in advance.

Kavin

[fiza gupta]

Amount= 5000
rate = 8%
interest = 5000*.08 = 400

interest is 6.5% of SP
400 = 6.5% of s.p
400 = .065*sp
=6153.8

SO E

[GMATGuruNY]

Hi GMATGuruNY ,

Can you please explain with the algebraic approach?

Many thanks in advance.

Kavin

8% interest on the $5000 bond = (8/100)(5000) = 400.
Since this value is equal to approximately 6.5% of the selling price, we get:
400 = (6.5/100)x
400 = (13/200)x
x = 80000/13 = more than 6100.

The correct answer is E.

[Jeff@TargetTestPrep]

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

A - $4063
B - $5323
C - $5351
D - $6000
E - $6154

E

We are given that a certain bond with a face value of $5,000 yielded 8% of its face value in interest. Thus, we can determine the interest as follows:

5,000 x 0.08 = 400

We also know that the $400 of interest was approximately 6.5% of the bond's selling price. Thus, we can create the following equation, where p = the bond's selling price:

400 = 0.065 x p

400/0.065 = p

400,000/65 = p

6,154 ≈ p

Answer: E