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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
If a sum of money grows to 144/121 times when invested for two years  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 47% (02:27) correct 53% (02:19) wrong based on 22 sessions

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If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A) 9 years
(B) 18 years
(C) 22 years
(D) 31 years
(E) 33 years

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Re: If a sum of money grows to 144/121 times when invested for two years  [#permalink]

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Bunuel wrote:
If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to trebleif invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A) 9 years
(B) 18 years
(C) 22 years
(D) 31 years
(E) 33 years

Bunuel please check highlighted part ; seems to be a typo error
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SVP  V
Joined: 26 Mar 2013
Posts: 2343
Re: If a sum of money grows to 144/121 times when invested for two years  [#permalink]

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Bunuel wrote:
If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to trebleif invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A) 9 years
(B) 18 years
(C) 22 years
(D) 31 years
(E) 33 years

Bunuel I think it should be 'triple'

Also, I think the OA is wrong.

Compound annually: Total = P (1+r/n)^nt...where p is original amount & r is interest rate & t is number of years & n: number of compounding annually.

Total = $$\frac{144}{121}$$P

$$\frac{144}{121}$$P = P (1+r)^2.......$$\frac{12}{11}$$= (1+r).........r = $$\frac{1}{11}$$

Apply in simple interest formula

Total = P * r * #of years

3P = P * $$\frac{1}{11}$$ * Y.............Y = 33

Answer must be E

Dear GMATPrepNow Brent,

Can you help and shed lught on the solution above?

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Re: If a sum of money grows to 144/121 times when invested for two years  [#permalink]

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Top Contributor
Mo2men wrote:
Bunuel wrote:
If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to trebleif invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A) 9 years
(B) 18 years
(C) 22 years
(D) 31 years
(E) 33 years

Bunuel I think it should be 'triple'

Also, I think the OA is wrong.

Compound annually: Total = P (1+r/n)^nt...where p is original amount & r is interest rate & t is number of years & n: number of compounding annually.

Total = $$\frac{144}{121}$$P

$$\frac{144}{121}$$P = P (1+r)^2.......$$\frac{12}{11}$$= (1+r).........r = $$\frac{1}{11}$$

Apply in simple interest formula

Total = P * r * #of years

3P = P * $$\frac{1}{11}$$ * Y.............Y = 33

Answer must be E

Dear GMATPrepNow Brent,

Can you help and shed lught on the solution above?

Be careful, the formula you stated "Total = P * r * #of years" is a formula for finding the INTEREST (not the total value of the investment)
There's also a problem with the 3P part of your equation.

Notice that, if we start with a $10 investment, and its value triples to$30, this means the investment received $20 in interest. We want the investment to go from P to 3P Well P + 2P = 3P So, we want the TOTAL INTEREST to equal 2P We get: 2P = (P)(interest rate)(#of years) Or: 2P = (P)(1/11)(x) Solve to get x = 22 Cheers, Brent _________________ SVP  V Joined: 26 Mar 2013 Posts: 2343 Re: If a sum of money grows to 144/121 times when invested for two years [#permalink] Show Tags GMATPrepNow wrote: Mo2men wrote: Bunuel wrote: If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to trebleif invested at the same rate of interest in a scheme where interest is computed using simple interest method? (A) 9 years (B) 18 years (C) 22 years (D) 31 years (E) 33 years Bunuel I think it should be 'triple' Also, I think the OA is wrong. Compound annually: Total = P (1+r/n)^nt...where p is original amount & r is interest rate & t is number of years & n: number of compounding annually. Total = $$\frac{144}{121}$$P $$\frac{144}{121}$$P = P (1+r)^2.......$$\frac{12}{11}$$= (1+r).........r = $$\frac{1}{11}$$ Apply in simple interest formula Total = P * r * #of years 3P = P * $$\frac{1}{11}$$ * Y.............Y = 33 Answer must be E Dear GMATPrepNow Brent, Can you help and shed lught on the solution above? Thanks in advance Be careful, the formula you stated "Total = P * r * #of years" is a formula for finding the INTEREST (not the total value of the investment) There's also a problem with the 3P part of your equation. Notice that, if we start with a$10 investment, and its value triples to $30, this means the investment received$20 in interest.

We want the investment to go from P to 3P
Well P + 2P = 3P

So, we want the TOTAL INTEREST to equal 2P
We get: 2P = (P)(interest rate)(#of years)
Or: 2P = (P)(1/11)(x)

Solve to get x = 22

Cheers,
Brent

Thanks GMATPrepNow Brent

Nicely explained as always Thanks a lot.

I treated the simple interest equation as the compound equation above it.
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Re: If a sum of money grows to 144/121 times when invested for two years  [#permalink]

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Bunuel wrote:
If a sum of money grows to 144/121 times when invested for two years in a scheme where interest is compounded annually, how long will the same sum of money take to treble if invested at the same rate of interest in a scheme where interest is computed using simple interest method?

(A) 9 years
(B) 18 years
(C) 22 years
(D) 31 years
(E) 33 years

We can let P = the principal and r = the interest rate and create the equation:

P(1 + r)^2= (144/121)P

(1 + r)^2 = 144/121

1 + r = √(144/121)

1 + r = 12/11

r = 1/11

Therefore, the annual interest rate is 1/11. If we let t = the number of years for the principal to triple using simple interest method with this rate, we can create the equation:

P + P(1/11)t = 3P

P(t/11) = 2P

t/11 = 2

t = 22

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If a sum of money grows to 144/121 times when invested for two years   [#permalink] 31 Jan 2019, 18:39
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