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# An investment of d dollars at k percent simple annual interest yields

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Intern
Joined: 24 Apr 2010
Posts: 26
An investment of d dollars at k percent simple annual interest yields  [#permalink]

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04 May 2010, 02:24
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Difficulty:

25% (medium)

Question Stats:

81% (01:24) correct 19% (01:49) wrong based on 247 sessions

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An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield$2,400 over a 3 year period?

A. (2d)/3
B. (3d)/4
C. (4d)/3
D. (3d)/2
E. (8d)/3

OPEN DISCUSSION OF THIS QUESTION IS HERE: an-investment-of-d-dollars-at-k-percent-simple-annual-106083.html
Manager
Joined: 24 Jul 2009
Posts: 244
Re: An investment of d dollars at k percent simple annual interest yields  [#permalink]

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04 May 2010, 02:42
perseverant wrote:
An investment of d dollars at k percent simple annual interes yields $600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate would yield$2400 of interest over a 3 year period?

a)(2d)/3
b)(3d)/4
c)(4d)/3
d)(3d)/2
e)(8d)/3

This is a question I got wrong in my GMATPrep test. Could someone help me get to the right answer?

Thanks!

IMHO E

case 1:

600 = (d * k * 2)/100
so, d*k = 30000 .............................(1)

Case 2:

Let the amount invested be "a"

so, 2400 = (a * k * 3)/100
a*k = 80000 .............................(2)

From (1) insert the value of k in (2)

a*(3000)/d = 80000
a = (8*d)/3
Intern
Joined: 09 Jan 2010
Posts: 27
Re: An investment of d dollars at k percent simple annual interest yields  [#permalink]

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04 May 2010, 02:47
hi perseverant,

first the prob states that

(P*N*R)/100 = I

(d*2*k)/100 = 600

d*k = 600 *50

Now try Substituting the answer choices since this is a variable in answer choice question such that the interest comes to 2400 $Lets try option e In this case P= 8d/3 N = 3 R = k (same rate) I = (8d/3 * 3* k) /100 = (8*d*k)/100 But d*k = 600*50 substitute above we get 8*600*50 /100 = 8*600*1/2 = 4*600 = 2400 Therfore the answer is E. whts the OA ?? Intern Joined: 24 Apr 2010 Posts: 26 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 04 May 2010, 03:03 Thank you guys, you both are correct, the OA is e. I tried to use the simple interest rate formula P*(1+r.t) since it's the only one I knew, but you both have used I= (P*N*R)/100. I guess Im not very clear on why simple interest rate formula would not be the right one to start off. Manager Joined: 12 Jan 2010 Posts: 245 Schools: DukeTuck,Kelogg,Darden Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 04 May 2010, 06:05 4 1 perseverant wrote: An investment of d dollars at k percent simple annual interes yields$600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate would yield $2400 of interest over a 3 year period? a)(2d)/3 b)(3d)/4 c)(4d)/3 d)(3d)/2 e)(8d)/3 This is a question I got wrong in my GMATPrep test. Could someone help me get to the right answer? Thanks! Hi its E, here is how i did it Currently the investment pays$600 in 2 years = $300/year what we need is$2400 in 3 years = $800 a year So the investment needs to be = 800/300 times the current investment = 8d/3. _________________ Run towards the things that make you uncomfortable daily. The greatest risk is not taking risks http://gmatclub.com/forum/from-690-to-730-q50-v38-97356.html Intern Joined: 24 Apr 2010 Posts: 26 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 04 May 2010, 10:23 Nice! I guess I didnt need to know any formula Intern Joined: 29 Jun 2011 Posts: 25 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 27 Aug 2011, 06:23 perseverant wrote: An investment of d dollars at k percent simple annual interes yields$600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate would yield $2400 of interest over a 3 year period? a)(2d)/3 b)(3d)/4 c)(4d)/3 d)(3d)/2 e)(8d)/3 This is a question I got wrong in my GMATPrep test. Could someone help me get to the right answer? Thanks! I got E but I'm not sure if my calculation is correct...quite weird. can anyone pls enlighten? thanks! My way: Case 1: d * k/100 * 2 = 600 (for 2 years period) Case 2: d * k/100 * 3 = 2400 (for 3 years period) So 2kd / 100 = 600 versus 3kd / 100 = 2400 => 2kd = 60000 : 3kd = 240000 => 2kd/60000 = 3kd/240000 => 180000kd = 480000kd =>3/8 kd => k = (8/3)d Retired Moderator Joined: 20 Dec 2010 Posts: 1820 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 27 Aug 2011, 06:33 miweekend wrote: perseverant wrote: An investment of d dollars at k percent simple annual interes yields$600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate would yield $2400 of interest over a 3 year period? a)(2d)/3 b)(3d)/4 c)(4d)/3 d)(3d)/2 e)(8d)/3 This is a question I got wrong in my GMATPrep test. Could someone help me get to the right answer? Thanks! I got E but I'm not sure if my calculation is correct...quite weird. can anyone pls enlighten? thanks! My way: Case 1: d * k/100 * 2 = 600 (for 2 years period) Case 2: d * k/100 * 3 = 2400 (for 3 years period) So 2kd / 100 = 600 versus 3kd / 100 = 2400 => 2kd = 60000 : 3kd = 240000 => 2kd/60000 = 3kd/240000 => 180000kd = 480000kd =>3/8 kd => k = (8/3)d I see that you got the answer right. I'd rather do it this way: $$d*\frac{k}{100}*2=600$$ $$k=\frac{30000}{d}$$---------------------1 We got our rate in terms of d; let the new principal be x; now, we take the other case: $$x*\frac{k}{100}*3=2400$$ $$x=\frac{80000}{k}$$ Write k in terms of d; $$x=\frac{80000d}{30000}=\frac{8d}{3}$$ Ans: "E" _________________ Manager Joined: 14 Mar 2011 Posts: 67 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 27 Aug 2011, 07:03 Most of Us got the Right answer, My Answer is also E, please find explanation below we know that Principle*No. of Years* rate of interest= Interest d*2*k/100 = 600 we get K=30000/d Now we know the interest rate k & interest=2400 but amount is not know let it be x, nos. of years 3 x *3*k/100 = 2400 xk=800*100 put the value of K we get x*30000/d=800*100 so x = 8/3*d Director Joined: 01 Feb 2011 Posts: 659 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 27 Aug 2011, 08:36 Simple Interest = PRT First Amount = d => P=d Rate of interest = k/100 time T = 2 => d*(k/100)(2) = 600 => k = 3*10^4/d Second Amount Rate of interest = k/100 time = 3 => P (k/100)(3) = 2400 => P(3*10^2/d)*3 = 2400 => P = 8d/3 Answer is E. Director Joined: 03 May 2007 Posts: 800 Schools: University of Chicago, Wharton School Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 27 Aug 2011, 18:40 perseverant wrote: An investment of d dollars at k percent simple annual interes yields$600 interest over a 2 year period. In terms of d, what dollar amount invested at the same rate would yield $2400 of interest over a 3 year period? a)(2d)/3 b)(3d)/4 c)(4d)/3 d)(3d)/2 e)(8d)/3 This is a question I got wrong in my GMATPrep test. Could someone help me get to the right answer? 2dk = 600 Lets make the interest part 2400. 3dk = 2400 2dk (1.5) m = 600 x 4 2dk (m) = 600 x 4/(1.5) 2dk (m) = 600 x 8/3 m = 8/3 i.e. the amount in terms of d is = 8d/3 Math Expert Joined: 02 Sep 2009 Posts: 51123 Re: An investment of d dollars at k percent simple annual interest yields [#permalink] ### Show Tags 02 Jan 2015, 04:08 perseverant wrote: An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 over a 3 year period? A. (2d)/3 B. (3d)/4 C. (4d)/3 D. (3d)/2 E. (8d)/3 Simple interest = principal * interest rate * time, where "principal" is the starting amount and "rate" is the interest rate at which the money grows per a given period of time (note: express the rate as a decimal in the formula). Time must be expressed in the same units used for time in the Rate. An investment of d dollars at k percent simple annual interest yields$600 over a 2 year period --> $$d*\frac{k}{100}*2=600$$ --> $$k=\frac{30,000}{d}$$

What (x) dollar amount invested at the same rate will yield \$2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$.

Or another way: In order interest to be 4 times more in 1.5 times longer time period then investment must be 4d/1.5=8d/3.

OPEN DISCUSSION OF THIS QUESTION IS HERE: an-investment-of-d-dollars-at-k-percent-simple-annual-106083.html
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Re: An investment of d dollars at k percent simple annual interest yields  [#permalink]

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11 Aug 2018, 07:33
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