Question

Ramona has a total of $5000 to invest. She puts part of it in an account paying 5% per year interest and the rest in a GIC paying 7.2% interest. If she has $349 in simple interest at the end of the year, how much was invested at each rate?

Answer 1

Let x represent the amount invested in the account paying 5% interest per year.
Let y represent the amount invested in the GIC paying 7.2% interest.
x + y = $5,000 ⇒ y = $5,000 - x
0.05x + 0.072 = $349 ⇒ (multiply by 1000 to get rid of decimals) ⇒
50x + 72y = $349,000
Then substitute the y equation into the second equation.
50x + 72 (5,000 - x ) = 349,000
50x + 360,000 - 72x = 349,000
50x - 72x = 349,000 - 360,000
-22x = -11,000 (divide both sides by -22)
x = 500
∴ the amount invested in the account paying 5% interest per year is $500.
Now solve for y.
x + y = 5,000
500 + y = 5,000
y = 5,000 - 500
y = 4,500
∴ the amount in the GIC paying 7.2% interest is $4,500.