Answer for this question

Question

Betsy a recent retiree requires $5,000 per year in extra income. She has $60,000 to invest and can invest in B-rated bonds paying 13% per year or a certificate of deposit (cd) paying 5% per year. How much money should be invested in each to realize exactly 5,000 in interest per year

Answer 1

.13B +.05(CD) = 5

.13B + .05(60-B) = 5

integers refer to thousands of dollars, 5 means $5,000, 60 means $60,000

.13 = 13%, .05 = 5%

.13B -.05B = 5-(.05)(60) = 5-3 =2

.08B =2

B = 2/.08 = 1/.04 = 25 for B rated bonds

CD =60-25 = 35 for Certificates of Deposit

Invest $25,000 in B bonds and $35,000 in CDs to get exactly $5,000 in interest

check the answers:

.13(25) +.05(35) = 3.25 + 1.75 = 5

5/60 = 1/12 = .08333...= 8 1/3 % interest= average interest. 5<8 1/3<13

13-8 1/3 = 4 2/3 =14/3

8 1/3 - 5 = 3 1/3 = 10/3

(14/3)/(10/3) = 14/10 = 7/5= 1.6

the amount invested at 5% is 7/5 = 1.4 times the amount invested at 13%. 35=1.4(25)

35/25 = 7/5= 1.4