Question

Betsy, a recent​ retiree, requires ​$ 6 comma 000 6,000 per year in extra income. She has ​$ 60 comma 000 60,000 to invest and can invest in​ B-rated bonds paying 15 15​% per year or in a certificate of deposit​ (CD) paying 5 5​% per year. How much money should be invested in each to realize exactly ​$ 6 comma 000 6,000 in interest per​ year?

Answer 1

Let the amount she invests in the B-rated bonds be x, and the amount she invested in the certificate of deposit be y.

Then,

x + y = 60,000 . . . . . . . (1)
0.15x + 0.05y = 6,000 . (2)

Multiplying the first equation by 0.15 gives:

0.15x + 0.15y = 9,000 . (3)

Subtracting equation (2) from equation (3) gives:

0.1y = 3,000

y = 3,000 / 0.1 = 30,000

From equation (1):

x + 30,000 = 60,000

x = 60,000 - 30,000 = 30,000

Therefore, the amount of money that should be invested in each to realize exactly ​$6,000 in interest per​ year is $30,000 each.