Betsy a recent retiree require 5000 per year in extra income

Betsy, a recent retiree, require $5,000 per year in extra income. She has $50,000 to invest and can invest in B-rated bonds paying 13% per year or in certificate of deposit (CD) paying 3% per year. How much money should be invest in each to realize exactly $5,000 in interest per year?

The amount of money invest at 13%=
The amount of money invested at 3%=

Solution

Quantity:

B + C = 50,000

Interest:

0.13B + 0.03C = 5000

Modify for elimination:

13B + 13C = 13*50,000

13B + 13C = 650000 ..............................(1)

13B + 3 C = 100*5000

13B + 3 C = 500000...............................(2)

Subtract and solve for \"C\":

10C = 3*50,000

C = 3*5000

C = $15,000 (amt. invested at 3%) [ Answer ]

Now pluginthe value of C in (2), we get :

13B + 3*15000 = 500000

13B + 45000 = 500000

13B = 500000 - 45000

13B = 455000

B = 35000

Hence B = $35,000 (amt. invested at 13%) [ Answer ]