Question

A retired woman has $280,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another riskier fund that has a 13% annual yield. How much should she invest in each fund if she would like to earn $28,000 per year from her investments?
9% fund $

13% fund $

Answer 1

Answer:

9% fund: $ 210,000

13% fund: $70,000

Step-by-step explanation:

As she wants to have a $28,000 annual return for her $280,000 investment, she is expecting a return rate of 10%:

$r=\dfrac{R}{C}=\dfrac{28,000}{280,000}=0.10$

If we call x the proportion of the capital in the 9% fund, then (1-x) is the proportion of the capital in the 13% fund,and the return of the combination has to be the expected return of 10%:

$0.09x+0.13(1-x)=0.10\\\\0.09x+0.13-0.13x=0.10\\\\-0.04x=0.10-0.13=-0.03\\\\x=\dfrac{0.03}{0.04}=0.75$

Then, we know that 75% of the capital should be invested in the 9% fund and 25% in the 13% fund.

This correspond to a capital of:

9% fund: 0.75*$280,000 = $ 210,000

13% fund: 0.25*$280,000 = $70,000