Fred invested 12,000.some 4% and some at 7% annual interest. If after a year he made $720 in interest, how much did he invest at each rate ?

Answer 1

There will be 2 equations and 2 unknowns in this problem.

Let x = amount of money invested at 4% (r = 4/100 = .04)

Let y = amount of money invested at 7% (r = 7/100 = .07)

Equation 1 is the quantity equation: x + y = 12,000

Equation 2 is the value equation: .04x + .07y = 720

Use substitution to solve. Rearrange equation 1: x = 12,000 - y

.04(12000 - y) + .07y = 720

480 -.04y + .07y = 720

.03y = 720 - 480 = 240

y = 240/.03 = $8000; x = 12,000 - 8000 = $4000.

He invested $4000 at 4% and $8000 at 7%.