Answer for this question

Question

Betsy a recent retiree requires $6,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 13% per year or a certificate of deposit (cd) paying 3% per year. How much money should be invested in each to realize exactly 6,000 in interest per year

Answer 1

.13x + .03(70-x) = 6

.13x-.03x = 6-2.1

.1x = 3.9

x = 3.9/.1 =39

$39,000 invested at 13% bonds

$31,000 invested at 3% CD's

to earn exactly $6,000 on $70,000

check the solution:

.13(39)+.03(31)

=5.07 + .93 = 6

average rate of return on the $70,000

= 6/70 = 3/35 = about 8.57%

3<8.57<13

13-8.57= 4.43

8.57-.3 = 5.57

5.57/4.43 = 39/31 = about 1.26

about 1.26 times more is invested at 13 than at 3%