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Interest Rate Word Problem

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Interest Rate Word Problem

by jk2010 » Mon Jan 03, 2011 8:23 am
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!
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by shovan85 » Mon Jan 03, 2011 8:44 am
jk2010 wrote: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
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by GMATGuruNY » Mon Jan 03, 2011 12:40 pm
jk2010 wrote: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.
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by melguy » Sat Jun 15, 2013 10:47 pm
GMATGuruNY wrote:
jk2010 wrote: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.
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by smkhan » Fri Sep 12, 2014 2:28 am
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.
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by Needgmat » Sun Oct 30, 2016 10:11 pm

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
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by fiza gupta » Mon Oct 31, 2016 2:08 am
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
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by GMATGuruNY » Mon Oct 31, 2016 2:47 am
Needgmat wrote:
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.
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by Jeff@TargetTestPrep » Tue Nov 01, 2016 5:16 am
jk2010 wrote: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

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