Question

Jolene invests her savings in two bank accounts, one paying 6 percent and the other paying 9 percent simple interest per year. She puts twice as much in the lower-yielding account because it is less risky. Her annual interest is 7266 dollars. How much did she invest at each rate?

Amount invested at 6 percent interest is $
Amount invested at 9 percent interest is $

Answer 1

Amount invested at 6 percent interest is $69,200

Amount invested at 9 percent interest is $34,600

Explanation:

Let the amount invested (or principal) at 6 percent interest be $2x

The principal(P) (amount invested) at 9 percent interest will be $x

Amount(A) = P(1 + rt)

Time(t) = one year = 1

Amount at 6% interest = 2x(1 + 0.06) = $2.12x

Interest accumulated = Amount - Principal = $2.12x - $2x = $0.12x

Amount at 9% interest = x(1 + 0.09) = $1.09x

Interest accumulated = Amount - Principal = $1.09x - $x = $0.09x

Total interest = $7,266

So, $0.12x + $0.09x = $7,266

$0.21x = $7,266

x =
`(7,266)/(0.21)` = $34,600

The principal (amount invested) at 9 percent interest rate is $34,600

The principal (amount invested) at 6 percent interest rate is 2 × $34,600 = $69,200