Chapter A.8, Problem 17AYU

To determine

To find: How much money should betsy invest in each to realize exactly $\$6000$ in interest per year.

Answer to Problem 17AYU

Invest $\$31250$ bonds and $\$18750$ bonds in CD.

Explanation of Solution

Given:

Betsy, a recent retiree, requires $\$6000$ per year in extra income. She has $\$50000$ to invest and can invest in B-rated bonds paying $15\%$ per year or in a certificate of deposit paying $7\%$ per year.

Calculation:

Clearly,

$X+Y=50,000, Y=50000-X$ and $0.15x+0.07y=6000$

Therefore, $0.15x+0.07\left(50000-X\right)=6000$.

So, $X=31250$ and $Y=18750$.

Therefore invest $\$31250$ bonds and 18750 bonds in CD.