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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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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
[Reveal] Spoiler: OA

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Re: Another simple one i guess... [#permalink]

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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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).

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.
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Re: Another simple one i guess... [#permalink]

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New post 10 Dec 2010, 11:38
Thanks. Didnt know the Simple interest thing.

+1 from me for all ur help.

thanks.
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Re: an investment of d dollars at k percent [#permalink]

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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 [#permalink]

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

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

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

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New post 09 Feb 2015, 12:27
Hi Bunuel,

If we take simple annual interest of 2% for $10,000 investment, for 2 years it will amount to $404.

How do we know "An investment of d dollars at k percent simple annual interest yields $600 over a 2 year period" = d*k/100 *2
and not similar to $404 calc?

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

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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)

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

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New post 09 Feb 2015, 16:20
Thanks Rich

I'll memorize that
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Re: An investment of d dollars at k percent simple annual [#permalink]

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New post 25 May 2015, 11:54
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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
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Re: An investment of d dollars at k percent simple annual [#permalink]

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New post 25 May 2015, 22:31
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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)

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

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

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New post 15 Dec 2015, 05:49
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)
\(\frac{8}{3}\)=\(\frac{x}{d}\) --> \(x=\frac{8}{3}*d\)
Answer E
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An investment of d dollars at k percent simple annual   [#permalink] 15 Dec 2015, 05:49
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