Interest Rate Word Problem

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jk2010: Senior | Next Rank: 100 Posts; Posts: 66; Joined: Wed Sep 29, 2010 8:41 am; Location: Washhington, DC; Thanked: 8 times

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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Source: Beat The GMAT — Problem Solving | Mon Jan 03, 2011 8:23 am

shovan85: Community Manager; Posts: 991; Joined: Thu Sep 23, 2010 6:19 amFollowed by: 24 members; Location: Bangalore, India; Thanked: 146 times

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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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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melguy: Master | Next Rank: 500 Posts; Posts: 335; Joined: Mon Mar 21, 2011 11:31 pmFollowed by: 2 members; Location: Australia / India; Thanked: 37 times

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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smkhan: Junior | Next Rank: 30 Posts; Posts: 17; Joined: Wed Apr 24, 2013 11:42 am

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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Needgmat: Master | Next Rank: 500 Posts; Posts: 234; Joined: Tue May 31, 2016 1:40 am; Thanked: 3 times

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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fiza gupta: Master | Next Rank: 500 Posts; Posts: 216; Joined: Sun Jul 31, 2016 9:55 pmFollowed by: 7 members; Location: Punjab; Thanked: 31 times

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

Fiza Gupta

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

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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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

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 â‰ˆ p

Answer: E

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Head of GMAT Instruction
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