An investment of d dollars at k percent simple annual

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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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.

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

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

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

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

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

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

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

Cheers,
Brent

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.
_________________

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
_________________

Simple Interest = P*r*t/100

From the first condition,

600 = d*k*2/100 .......(i)

Let the principal invested for 3 years be x

Thus, 2400 = x*k*3/100 .....(ii)

After dividing (ii) by (i),

4 = x*3/d*2

Thus, x = 8d/3

Thus, the correct option is E.

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