Hi vrn2vw,

To start, we can simplify the equations by focusing on the INTEREST ONLY.

D dollars at K percent simple interest for 2 years = $600

D(K/100)(2) = 600

This becomes....

DK = 30,000

Now we have to look at....

E dollars at K percent simple interest for 3 years = $2400

E(K/100)(3) = 2400

EK = 80,000

So, we need to go from 30,000 to 80,000. What do we need to multiply by? 8/3.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

"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 interest 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 [spoiler]E, which can be written as (8/3)d,[/spoiler] 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

vrn2vw wrote:An investment of d dollars at k percent simple annual interest yields $600 interest over a 2-year period. In terms of d, what dollar amount invested at the same rate will yield $2,400 interest over a 3 year period?

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

Can someone explain this one? OA is 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