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# A sum of money is invested at simple interest, partly at 4% and remain

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Math Expert
Joined: 02 Sep 2009
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A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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27 Sep 2018, 04:37
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Difficulty:

35% (medium)

Question Stats:

81% (01:33) correct 19% (03:38) wrong based on 27 sessions

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A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is$18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500 (B)$6000
(C) $7000 (D)$10500
(E) $11000 _________________ CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2711 Location: India GMAT: INSIGHT WE: Education (Education) Re: A sum of money is invested at simple interest, partly at 4% and remain [#permalink] ### Show Tags 27 Sep 2018, 05:20 Bunuel wrote: A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was$2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest? (A)$5500
(B) $6000 (C)$7000
(D) $10500 (E)$11000

Since it's a simple interest case so the interest for each year on each sum will remain constant

and 4% for 1 year = 8% for two years
and 7% for 1 year = 14% for two years

Let, SUm invested at 4% = x
i.e.e Sum invested at 7% = 18000-x

$$(8/100)*x + (14/100)*(18000-x) = 2100$$

i.e. 8x+252000-14x = 210000

i.e. 6x = 42000

i.e. x = 7000

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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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27 Sep 2018, 07:54
Given that the total interest in 2 years is 2,100. We can try picking from the answer choices.

Since total investment is 18,000 we pick investment for 4% to be 6,000

We try 6,000 * 4/100 = 240

12,000 * 7/100 = 840

If we add them we get 1,080 * 2 = 2,160 in 2 years making it larger than the desired interest.

From this we should be able to realize that we should increase the amount allotted for the 4%

And the answer would be C.

7,000 * 4/100 = 280

11,000 * 7/100 = 770

Added together we get 1,050 * 2 = 2,100

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Re: A sum of money is invested at simple interest, partly at 4% and remain  [#permalink]

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28 Sep 2018, 02:33
Bunuel wrote:
A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was $2100. If the total investment is$18000, what was the sum of money invested at 4% annual rate of interest?

(A) $5500 (B)$6000
(C) $7000 (D)$10500
(E) $11000 So my approach was to calculate the rate of interest which gives 2100 as interest. (18000 * 2 * x)/100 = 2100 rate comes out to be (35/6) 4 -------------------- 7 ----------35/6-------- 7/6------------------11/6 amount invested at 4% = (7/6) * (6/18) = (7/18) so amount is 7000. Director Status: Come! Fall in Love with Learning! Joined: 05 Jan 2017 Posts: 506 Location: India Re: A sum of money is invested at simple interest, partly at 4% and remain [#permalink] ### Show Tags 28 Sep 2018, 03:33 Hi, It is a simple interest question, so there is no big calculations here. We can eliminate the answer choices D and E. Because given, Total investment = 18000 And total interest earned = 2100. For a moment, let’s assume the amount is equally distributed. Then, 4% of 9000 + 7% of 9000 = 360 + 630 = 990 for one year. Total amount for two years is 1980. Which is less than the actual total interest(2100) given in the question. So the amount distributed in 4% should be lesser than the amount invested in 7%. Hence we can eliminate D and E. Answer as to be either A, B and C. Also the amount 1980 was not too far from 2100, then the best answer choice to try would be answer choice C. So, 4% of 7000 + 7% of 11000 = 280 + 770 = 1050 for one year. Total amount for two years is 2100. Which matches the amount given in the question. So the answer is C. Hope it helps. _________________ GMAT Mentors Target Test Prep Representative Status: Founder & CEO Affiliations: Target Test Prep Joined: 14 Oct 2015 Posts: 4278 Location: United States (CA) Re: A sum of money is invested at simple interest, partly at 4% and remain [#permalink] ### Show Tags 02 Oct 2018, 18:52 Bunuel wrote: A sum of money is invested at simple interest, partly at 4% and remaining at 7% annual rates of interest. After two years, the total interest obtained was$2100. If the total investment is $18000, what was the sum of money invested at 4% annual rate of interest? (A)$5500
(B) $6000 (C)$7000
(D) $10500 (E)$11000

We can let the amount of money invested at 4% interest = n. The amount invested at 7% is (18,000 - n). We can create the following equation:

2 x 0.04n + 2 x 0.07(18,000 - n) = 2,100

0.08n + 2,520 - 0.14n = 2,100

-0.06n = -420

n = 7,000

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Re: A sum of money is invested at simple interest, partly at 4% and remain &nbs [#permalink] 02 Oct 2018, 18:52
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# A sum of money is invested at simple interest, partly at 4% and remain

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