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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?
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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).
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.
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.
Re: An investment of d dollars at k percent simple annual [#permalink]
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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?
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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6
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...
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...
Re: An investment of d dollars at k percent simple annual [#permalink]
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12 Jul 2015, 20:01
5
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.
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) \(\frac{8}{3}\)=\(\frac{x}{d}\) --> \(x=\frac{8}{3}*d\) Answer E
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Re: An investment of d dollars at k percent simple annual [#permalink]
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13 Jan 2018, 07:43
Top Contributor
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] Answer = E
Re: An investment of d dollars at k percent simple annual [#permalink]
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15 Mar 2018, 19:06
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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).
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.
Bunuel.
I'm more interested in the "Another way" to solve it. I get the "4 times more" but I can't get to the "1.5 times longer". How do you calculate this?
Thanks.
Best.
_________________
"The stock market is filled with individuals who know the price of everything, but the value of nothing." - Philip Fisher
Re: An investment of d dollars at k percent simple annual [#permalink]
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15 Mar 2018, 20:52
MarkHanna 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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).
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.
Bunuel.
I'm more interested in the "Another way" to solve it. I get the "4 times more" but I can't get to the "1.5 times longer". How do you calculate this?
Thanks.
Best.
(3 year period)/(2 year period) = 1.5.
_________________
Re: An investment of d dollars at k percent simple annual [#permalink]
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19 Mar 2018, 16:14
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
However, we are being asked for the dollar amount invested, in terms of d, at the annual interest rate of k percent that will yield $2,400 interest over a 3-year period. If we let this dollar amount be x, then
2,400 = x(k/100)(3)
800 = xk/100
xk = 80,000
Since dk = 30,000 and xk = 80,000, k = 30,000/d and k = 80,000/x. Thus, we can equate 30,000/d and 80,000/x and isolate x.
30,000/d = 80,000/x
30,000x = 80,000d
3x = 8d
x = 8d/3
Answer: E
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Re: An investment of d dollars at k percent simple annual [#permalink]
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30 May 2018, 12:35
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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).
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.
An investment of d dollars at k percent simple annual [#permalink]
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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 --> \(x*\frac{k}{100}*3=2,400\) --> \(x*\frac{30,000}{100d}*3=2,400\) --> \(x=\frac{8d}{3}\).
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.
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