A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments?
A)$11,700
B)$16,900
C)$57,500
D)$72,500
E)$113,100

Question

A retired woman has $130,000 to invest. She has chosen one relatively safe investment fund that has an annual yield of 9% and another, riskier one that has an annual yield of 13%. How much should she invest in the fund yielding 9% if she would like to earn $14,000 per year from her investments? ​
A)$11,700
B)$16,900
C)$57,500
D)$72,500
E)$113,100

Quizplus · Accepted Answer

Let x be the amount invested in the fund yielding 9%. Then the amount invested in the riskier fund is 130,000 - x.
The annual income from the 9% fund is 0.09x and the annual income from the riskier fund is 0.13(130,000 - x) = 16,900 - 0.13x.
The total annual income is the sum of these two amounts, which is 0.09x + 16,900 - 0.13x = 16,900 - 0.04x.
If she wants to earn $14,000 per year from her investments, then we must have:

16,900 - 0.04x = 14,000
0.04x = 2,900
x = 72,500

Therefore, she should invest $72,500 in the 9% fund and the remaining amount in the riskier fund.

A Retired Woman Has $130,000 to Invest