Simple Interest GMAT, GRE Problem Solving Guide

All interest referred to below is simple interest. The annual amount of interest paid on an investment is found by multiplying the amount invested (the principal) by the percent of interest (the rate).

Example:

Sam invested some of his money in a bank paying 4% interest annually and a second amount, $500 less than the first, in a bank paying 6% interest. If her annual income from both investments was $50, how much money did Sam invest at 6%?

Solution:

As this is a non-ratio algebraic problem, we can handle this with a Distance = Rate x Time chart. Only we'll need an analogy for our names. Let's use: 

PRINCIPAL · RATE = INTEREST INCOME

Let's put it together algebraically.

x = amount invested at 4%x – 500 = amount invested at 6%
.04x = annual interest from 4% investment
.06(x – 500) = annual interest from 6% investment .04x + .06(x – 500) = 50

Multiply by 100 to remove decimals.

4x + 6(x − 500)= 5000 4x + 6x − 3000 = 5000 10x = 8000
x = 800x − 500 = 300

Sam invested $300 at 6%.

Let's try another using our matrix method

Jill invested $7200, part at 4% and the rest at 5%. If the annual income from both investments was the same, find her total annual income from these investments.

1. (A)  $160
2. (B)  $320
3. (C)  $4000
4. (D)  $3200
5. (E)  $1200
   
   

Let x = amount invested at 4%

7200 − x = amount invested at 5% .04x =.05(7200-x)

Multiply by 100 to eliminate decimals.

4x = 5(7200 − x)4x = 36,000 − 5x9x = 36,000
x = 4000
Her income is .04(4000) + .05(3200). 

$320.