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Peter invested a certain sum of money in a simple interest bond whose

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Peter invested a certain sum of money in a simple interest bond whose [#permalink]

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New post 03 Oct 2009, 04:17
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Question Stats:

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Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?

A. 12%
B. 12.5%
C. 6.67%
D. 6.25%
E. 8.33%
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Jul 2015, 10:21, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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New post 03 Oct 2009, 08:50
Economist wrote:
Peter invested a certain sum of money in a simple interest bond whose value grew to $300 at the end of 3 years and to $ 400 at the end of another 5 years. What was the rate of interest in which he invested his sum?

1. 12%
2. 12.5%
3. 6.67%
4. 6.25%
5. 8.33%

Simple, but there is a small trap in such SI problems, I fell into it..try it out:)


Took me time to figure out but the trap is "another 5 years". So overall, at the end of 8 years, the value grew to $400. The OA is E.
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New post 03 Oct 2009, 23:36
Just to make it clear to myself - am I right in formulating?

We have two equations:

400 = PV + 8*PV*r
300 = PV + 3*PV*r

Thus we get \(PV = \frac{300}{1+3r}\) then substiture this back into another equation and find r.

Tricky indeed, thanks for providing a good practice questions, Economist!

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New post 04 Oct 2009, 04:29
arkadiyua wrote:
Just to make it clear to myself - am I right in formulating?

We have two equations:

400 = PV + 8*PV*r
300 = PV + 3*PV*r

Thus we get \(PV = \frac{300}{1+3r}\) then substiture this back into another equation and find r.

Tricky indeed, thanks for providing a good practice questions, Economist!


No need to complicate with equations.
Since it is SI, we just need to divide the total interest earned by the number of years( because
a. in case of simple interest the interest earned each year will be the SAME and
b. in case of simple interest there is no interest on interest earned
)

Hence, 100 is earned over 5 years, so each year 20 is earned.
Now comes the tricky part,
I thought...hmmm..i know the amount invested=300, i know the interest earned=20 and i know the period=5 years, so let me apply the famous I = PRT/100 formula.

HOWEVER, interest is ALWAYS calculated on the PRINCIPAL invested, so we cannot take amount invested as 300 and proceed.

So we need to find the principal invested at the beginning which is 300-(20*3) = 240. Now we can apply I = PRT/100 with P=240, T=3, I = 60 to find R.

Sometimes such small observations help in avoiding silly mistakes :)

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New post 12 Oct 2009, 05:43
Economist wrote:
arkadiyua wrote:
Just to make it clear to myself - am I right in formulating?

We have two equations:

400 = PV + 8*PV*r
300 = PV + 3*PV*r

Thus we get \(PV = \frac{300}{1+3r}\) then substiture this back into another equation and find r.

Tricky indeed, thanks for providing a good practice questions, Economist!


No need to complicate with equations.
Since it is SI, we just need to divide the total interest earned by the number of years( because
a. in case of simple interest the interest earned each year will be the SAME and
b. in case of simple interest there is no interest on interest earned
)

Hence, 100 is earned over 5 years, so each year 20 is earned.
Now comes the tricky part,
I thought...hmmm..i know the amount invested=300, i know the interest earned=20 and i know the period=5 years, so let me apply the famous I = PRT/100 formula.

HOWEVER, interest is ALWAYS calculated on the PRINCIPAL invested, so we cannot take amount invested as 300 and proceed.

So we need to find the principal invested at the beginning which is 300-(20*3) = 240. Now we can apply I = PRT/100 with P=240, T=3, I = 60 to find R.

Sometimes such small observations help in avoiding silly mistakes :)


Economist, Hi

Thanks for the explanation but it seems I have trouble with counting interest problems.. Can you please just explain it once more( step by step). I faced one problem of these at the beginning of my first GMAT and failed to get it right.. I am having the GMAT againa fter a week . thanks in advance

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New post 13 Oct 2009, 02:09
Hi,

I got the answer as 6.25%. Kindly explain why wil it be 8.33%. Can't seem to get my head around it.. Thnx

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Hi,

I got the answer as 6.25%. Kindly explain why wil it be 8.33%. Can't seem to get my head around it.. Thnx


Will try to explain the best I can :wink:
Lets assume the Principal Amount (initial amount invested) to be P
rate of interest to be "R" and time as T. We need to find R

Now After a time of 3years the principal P amounts to $300 and after a time of 8years ( question says after another 5years so 3+5) P becomes $400.
Formulating the above data
Amount (A1) at end of 3years
A1= P(1 + 3R/100) = 300

Amount (A2) at end of 8years
A2 = P(1 + 8R/100) = 400

Dividing A2 by A1 we get
(1 + 8R/100)/(1 + 3R/100) = 4/3

after cross multiplication we are left with 12R =100 which gives R = 8.33%

Hope this helps

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New post 13 Oct 2009, 12:01
got it thnx :wink:
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New post 13 Oct 2009, 12:11
OMG! if you don't read the word "another" - u r gone

So this is a test to attentiveness in reading more than your Quant skills :P
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In 5 years the value went form 300 to 400, a total of $100. This is 20 per year.

In the 3 years early the investment added (3 x 20) = 60 dollars, so it started with 300 - 60 = 240.


20/240 = 1/12 = 8.33%

No need to do the calculation of 1/12. It is non repeating and closer to 10% (1/10) than 5% (1/20)
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New post 07 Sep 2017, 17:34
Let x be the capital invested and y, the interest rate. Thus:

\(3xy + x = 300\)
\(8xy + x = 400\)

Solving it we'll get:

\(x = 240\)
\(y = 1/12\)

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New post 12 Sep 2017, 02:03
Amount from start of 1st and till end of 3rd year=$300
Amount from 1st year till end of 8th year=$400
From 3rd to 8th-year(5 years) Interest earned=$100.
Per year Interest earned=100/5=$20.
Since this is simple interest every year interest earned is $20 then in 8 years Interest earned=$160
Principal=400-160=240.

Total return in 8 years=\(\frac{160}{240}*100\)=66.66%

Per year return=\(\frac{66.66}{8}\)=8.33%

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Re: Peter invested a certain sum of money in a simple interest bond whose [#permalink]

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New post 14 Sep 2017, 06:10
JimGMATAnswers wrote:
In 5 years the value went form 300 to 400, a total of $100. This is 20 per year.

In the 3 years early the investment added (3 x 20) = 60 dollars, so it started with 300 - 60 = 240.


20/240 = 1/12 = 8.33%

No need to do the calculation of 1/12. It is non repeating and closer to 10% (1/10) than 5% (1/20)



Very nice method. I solved it using x's and y's. :-)

So what I understood is that the interest is same for 8 years. That is why you have calculated 60 (3*20).

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Re: Peter invested a certain sum of money in a simple interest bond whose   [#permalink] 14 Sep 2017, 06:10
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