# 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 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

## Explanation: An investment of d dollars at k percent…

There’s a difference between simple interest and compound interest. Simple interest is, well, simpler. To get the interest earned you just multiply the interest rate by the base year by whatever number of periods you have. Let’s start by defining the question: In terms of d, what dollar amount invested at the same rate will yield \$2,400 over a 3 year period?

It looks like we’re given some information to create an equation and then we need to scale that equation up to \$2400/3 years.

So we start with two periods (two year period with annual interest) and can write out: 2(d*k/100) = 600.

But we want a three year period so you can just multiple both sides by 1.5 to yield: 3(d*k/100) = 900.

Now we need to yield \$2400 in that three year time period. So what do we need to multiply 900 by to get 2400? Just divide 2400 by 900 and you end up with 8/3. We know we’re keeping interest rate stable and just changing (increasing) the d dollars invested to hit the 2400. So we multiply d by 8/3. So 8d/3 dollars would get us there.

## Explanation Diagram  