Problem Solving

An investment of d dollars at k percent simple 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

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.

So, 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

Hi Mathsbuddy,

First off, you can simplify your 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