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27 Sep 2018, 05:34
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:27) correct 45% (02:12) wrong based on 71 sessions

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A sum of money invested under simple interest, amounts to $1200 in three years and$1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%

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02 Oct 2018, 02:12
Bunuel wrote:
A sum of money invested under simple interest, amounts to $1200 in three years and$1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%

Is there any other way (one that is using simple annual interest rate equation) to solve this one?
I am struggling with setting up the right equation.

Intern
Joined: 27 Apr 2018
Posts: 17
Location: India
Schools: CBS '21, Marshall '21
GMAT 1: 600 Q44 V29
GPA: 3.9

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05 Oct 2018, 06:04
1
Hey garvitbh11

Formula used:
$$A = P + SI$$ where A - Amount, P - Principal, and SI - Simple interest
$$SI = \frac{P*N*R}{100}$$ where P - Principal, N - number of years and R - rate of interest

$$P + \frac{3*P*R}{100} = 1200$$ (which is the amount in 3 year)
$$P + \frac{3*P*R}{100} + \frac{2*P*R}{100} = 1500$$ (which is the amount in 5 year)

From these two equations, you can figure the interest in 2 years in $300. Here's the thing about simple interest - it remains constant from year '1' to year 'n'. So, the SI for 1 year is $$\frac{300}{2} = 150$$ In 5 years the total interest is$750(5*150) and the principal(on which interest is calculated) is $750. Therefore, the rate at which the money was invested is $$\frac{150}{750} * 100 = 20$$%(Option C) Hope that helps! _________________ You've got what it takes, but it will take everything you've got Intern Joined: 27 Apr 2018 Posts: 17 Location: India Concentration: Finance, International Business Schools: CBS '21, Marshall '21 GMAT 1: 600 Q44 V29 GPA: 3.9 Re: A sum of money invested under simple interest, amounts to$1200 in thr  [#permalink]

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05 Oct 2018, 06:47
pushpitkc wrote:
Hey garvitbh11

Formula used:
$$A = P + SI$$ where A - Amount, P - Principal, and SI - Simple interest
$$SI = \frac{P*N*R}{100}$$ where P - Principal, N - number of years and R - rate of interest

$$P + \frac{3*P*R}{100} = 1200$$ (which is the amount in 3 year)
$$P + \frac{3*P*R}{100} + \frac{2*P*R}{100} = 1500$$ (which is the amount in 5 year)

From these two equations, you can figure the interest in 2 years in $300. Here's the thing about simple interest - it remains constant from year '1' to year 'n'. So, the SI for 1 year is $$\frac{300}{2} = 150$$ In 5 years the total interest is$750(5*150) and the principal(on which interest is calculated) is $750. Therefore, the rate at which the money was invested is $$\frac{150}{750} * 100 = 20$$%(Option C) Hope that helps! Thank you so much... now I know where I was wrong. Intern Joined: 05 Oct 2017 Posts: 10 Re: A sum of money invested under simple interest, amounts to$1200 in thr  [#permalink]

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08 Oct 2018, 02:14
In 5 years the total interest is $750(5*150) and the principal(on which interest is calculated) is$750.
How principal is 750??
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Re: A sum of money invested under simple interest, amounts to $1200 in thr [#permalink] ### Show Tags 09 Oct 2018, 10:39 Bunuel wrote: A sum of money invested under simple interest, amounts to$1200 in three years and $1500 in five years. What is the rate at which the sum of money was invested? (A) 10% (B) 15% (C) 20% (D) 25% (E) 45% We can let P = the principal and r = the annual interest rate. We see that after 3 years, the investment has earned P x r x 3 dollars in interest, and the interest earned is added to the principal, and this total amount is 1200: P + P x r x 3 = 1200 P(1 + 3r) = 1200 → Eq. 1 And, similarly, we have: P + P x r x 5 = 1500 P(1 + 5r) = 1500 → Eq. 2 Dividing Eq. 1 by Eq. 2, we have: (1 + 3r)/(1 + 5r) = 1200/1500 (1 + 3r)/(1 + 5r) = 4/5 5(1 + 3r) = 4(1 + 5r) 5 + 15r = 4 + 20r 1 = 5r r = 1/5 = 20% Answer: C _________________ # Scott Woodbury-Stewart Founder and CEO Scott@TargetTestPrep.com 122 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: A sum of money invested under simple interest, amounts to$1200 in thr   [#permalink] 09 Oct 2018, 10:39
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