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# An investment of d dollars at k percent simple annual

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An investment of d dollars at k percent simple annual  [#permalink]

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10 Dec 2010, 11:16
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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
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An investment of d dollars at k percent simple annual  [#permalink]

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10 Dec 2010, 11:34
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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$2,4,00 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.

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Re: An investment of d dollars at k percent  [#permalink]

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06 Feb 2012, 02:01
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Since you want to earn 4 times more interest in 1.5 times the current time period, the answer will be 4d/1.5 or 8d/3
##### General Discussion
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Re: An investment of d dollars at k percent simple annual  [#permalink]

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12 Jul 2015, 20:01
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Simple way to solve it -
600 dollars in 2 years means 300 dollars in 1 year.
To get 2400 dollars' it will take 8 years.
To get 2400 in 3 years, we need 8/3 times money. Answer is E.
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Re: An investment of d dollars at k percent simple annual  [#permalink]

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09 Feb 2015, 13:22
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Hi nitestr,

The GMAT will likely ask you to deal with an "interest formula" question once or twice, so you need to note the wording of the prompt and you need to know the formulas for simple interest and compound interest.

Simple Interest = (Principal)(1 + RT)

Compound Interest = (Principal)(1 + R)^T

R = interest rate written as a decimal
T = length of time (usually years)

So, if we calculate 2% simple interest on a $10,000 principal over 2 years, we'll have... (10,000)(1 + (.02)(2)) (10,000)(1.04) = 10,400 The interest = 400 (not 404) GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 15661 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 25 May 2015, 22:31 3 Hi SD007, If you want to calculate the amount of simple interest generated, then YES, the calculation is... (Principal)(RT) If you're interested in the TOTAL amount of money (e.g. in a bank account) AFTER the simple interest is generated, then the calculation is.... (Principal)(1 + RT) GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at: Rich.C@empowergmat.com The Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★ GMAT Club Legend Joined: 12 Sep 2015 Posts: 4125 Location: Canada Re: An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 13 Jan 2018, 07:43 2 1 Top Contributor 1 144144 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 An investment of d dollars at k percent simple annual interest yields$600 over a 2-year period.
In other words, an investment of d dollars yields $300 in interest each year. What dollar amount invested at the same rate will yield$2,400 interest over a 3-year period?
In other words, how much money must we invest to earn $800 in interest EACH YEAR? If a d dollar investment yields$300 in interest EACH YEAR, then:
- a 2d dollar investment would yield $600 (2 times$300) in interest EACH YEAR
- a 3d dollar investment would yield $900 (3 times$300) in interest EACH YEAR
- a 4d dollar investment would yield $1200 (4 times$300) in interest EACH YEAR
- etc.

From here there are two approaches.

APPROACH #1
We want the ANNUAL interest to be $800. This means we must invest an amount that is BETWEEN 2d dollars and 3d dollars [since$800 is BETWEEN $600 and$900].
When we check the answer choices, only E, which can be written as (8/3)d, is BETWEEN 2d dollars and 3d
So, the correct answer must be E

APPROACH #2
To increase the ANNUAL interest from $300 to$800, we must invest 800/300 TIMES as much money.
800/300 = 8/3, so we must invest (8/3)d dollars [aka 8d/3 dollars]

Cheers,
Brent
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Re: an investment of d dollars at k percent  [#permalink]

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18 Jun 2011, 07:58
1
WishMasterUA wrote:
an investment of d dollars at k percent simple annual interest yield $600 interest over a 2-year period. in term of d, what dollar amount invested at the same rate will yild$2400 interest income over a 3-year period?
1) 2d/3
2) 3d/4
3) 4d/3
4) 3d/2
5) 8d/3

Please explain in detail how to solve this problem.

simple interest = PNR/100
dk2=600
d = 300/k
thus
(x*300/k)*k*3= 2400
X= 2400/900= 24/9 = 8/3

hence E
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Re: An investment of d dollars at k percent simple annual  [#permalink]

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10 Jun 2013, 05:09
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

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Re: An investment of d dollars at k percent simple annual  [#permalink]

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25 May 2015, 11:54
1
EMPOWERgmatRichC wrote:
Hi nitestr,

The GMAT will likely ask you to deal with an "interest formula" question once or twice, so you need to note the wording of the prompt and you need to know the formulas for simple interest and compound interest.

Simple Interest = (Principal)(1 + RT)

Compound Interest = (Principal)(1 + R)^T

R = interest rate written as a decimal
T = length of time (usually years)

So, if we calculate 2% simple interest on a $10,000 principal over 2 years, we'll have... (10,000)(1 + (.02)(2)) (10,000)(1.04) = 10,400 The interest = 400 (not 404) GMAT assassins aren't born, they're made, Rich Hi Rich, The formula for the Simple interest is S.I = Principal (RT) no ? Thanks for your clarification. Regards S Senior Manager Joined: 10 Mar 2013 Posts: 461 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A$)
GMAT 1: 580 Q46 V24
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An investment of d dollars at k percent simple annual  [#permalink]

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15 Dec 2015, 05:49
1
1
144144 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

Hi guys, I just did my first CAT and this one was the first question that I answered correctly.
We don't need to involve any intetrest formulas at all here: the ratio of interest earnings per year = $$\frac{800}{300} = \frac{8}{3}$$ so the ratio of the investment that generates 2400 (let it be X) to D is the same (interest rate remains the same)
$$\frac{8}{3}$$=$$\frac{x}{d}$$ --> $$x=\frac{8}{3}*d$$
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Re: An investment of d dollars at k percent simple annual  [#permalink]

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19 Mar 2018, 16:14
1
144144 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

Recall that the amount of simple interest, I, is equal to the principal, P, times the annual interest rate, r, times the number of years, t. That is, I = Prt.

We are given that I = 600, P = d, r = k/100 and t = 2, so we have:

600 = d(k/100)(2)

300 = dk/100

dk = 30,000

What (x) dollar amount invested at the same rate will yield $2,400 over a 3 year period --> $$x*\frac{k}{100}*3=2,400$$ --> $$x*\frac{30,000}{100d}*3=2,400$$ --> $$x=\frac{8d}{3}$$. Answer: E. 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. Answer: E. hi pushpitkc - one question, why do we multiply by 2 like this $$d*\frac{k}{100}*2=600$$ shoudnt we put 2 as exponent as per formula $$600 = d(1+\frac{k}{100})^2$$ can you explain why am i thining so ? thankns! D Senior PS Moderator Joined: 26 Feb 2016 Posts: 3300 Location: India GPA: 3.12 An investment of d dollars at k percent simple annual [#permalink] ### Show Tags 30 May 2018, 12:45 1 dave13 wrote: Bunuel 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 $2,4,00 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.

hi pushpitkc -

one question, why do we multiply by 2 like this $$d*\frac{k}{100}*2=600$$ shoudnt we put 2 as exponent as per formula $$600 = d(1+\frac{k}{100})^2$$

can you explain why am i thining so ?

thankns!
D

Hey dave13

This problem deals with simple interest.
The formula for simple interest - Principal * Interest * $$\frac{R}{100}$$ where R is Rate of interest

Hope this helps you!
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An investment of d dollars at k percent simple annual   [#permalink] 30 May 2018, 12:45

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