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27 Sep 2018, 04:34
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Difficulty:

65% (hard)

Question Stats:

49% (01:52) correct 51% (01:31) wrong based on 65 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, 01:12
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, 05:04
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, 05:47
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: 04 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, 01:14
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, 09:39 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 GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Re: A sum of money invested under simple interest, amounts to$1200 in thr &nbs [#permalink] 09 Oct 2018, 09:39
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