Question

Betsy, a recent retiree, requires 5,000 per year in extra income. She has $70,000 to invest and can invest in B rated bonds paying 13% per year or in a certificate of deposit (CD) paying 5% per year. How much should be invested in each to realize exactly $5,000 in interest per year?

Answer 1

b = amount invested in B bonds

c = amount invested in CDs

so.. she's got $70000 burning a hole in her pocket and she wants to invest them to get a yield of 5000 in interest from both of them.

we know that, whatever "c" and "b" are, we  know that b + c = 70,000.

how much is 13% of b? well, (13/100) * b, or 0.13b
how much is 5% of c?  well, (5/100) * a, or 0.05c

we know that, the yield or interest earned from them, must be 5000, thus 0.13b + 0.05c = 5000.

$\bf \begin{cases} b+c=7000\implies \boxed{c}=70000-b\\ 0.13b+0.05c=5000\\ ----------\\ 0.13b+0.05\left( \boxed{70000-b} \right)=5000 \end{cases} \\\\\\ 0.13b-0.05b+3500=5000\implies 0.08b=1500\implies b=\cfrac{1500}{0.8} \\\\\\ b=18750$

how much did she invest in CDs?  well, c = 70000 - b.

Answer 2

Betsy a recent retiree,requires $5,000 per year in extra income. She has $70,000 to invest and can invest in B-rated bonds paying 15% per year or in a certificate of deposit (CD) paying 7% a year. How much should be invested in each to realize exactly $5,000 in interest per year?

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Equation:

interest + interest = interest

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0.15x + 0.07(70000-x) = 5000

Multiply thru by 100 to get:

15x + 7*70000-7x = 500000