You invested ​$13,000 in two accounts paying 3 % and 6 % annual​ interest, respectively. If the total interest earned for the year was $ 660 comma how much was invested at each​ rate?

Answer 1

Let n=amount invested at 3% rate

Let m=amount invested at 6% rate

We need 2 equations: one for the amount invested, one for the interest earned.

Amount invested: n + m = 13,000

Interest earned: 0.03n + 0.06m = 660

Solve these (multiply the bottom equation by 100 and the top equation by -3)

-3n + (-3)m = -39,000

3n + 6m = 66,000

Now add vertically and eliminate the n variable

3m = 27,000

Divide both sides by 3.

m = $9,000 (the amount invested at 6%)



n = what remains of the $13,000 investment, so

n = $4,000 (the amount invested at 3%)