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

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03 Oct 2009, 04:17

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E

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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?

Schools: LBS, INSEAD, IMD, ISB - Anything with just 1 yr program.

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

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

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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

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

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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

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

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

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13 Oct 2009, 05:01

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knownothingaboutgmat wrote:

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 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%

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

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17 Jul 2015, 09:44

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

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17 Jul 2015, 10:32

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

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10 Oct 2016, 16:08

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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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%

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