Question

A retired woman has $200,000 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 $20,000 per year from her investments?

Answer 1

To earn $20,000 per year from her investments, the retired woman should invest approximately $184,614.16 in the safe fund and $15,385.84 in the riskier fund.

Step-by-step explanation:

To determine how much the retired woman should invest in each fund, we can set up a system of equations. Let's assume she invests $x in the safe fund and $y in the riskier fund. The total investment is $200,000, so x + y = 200,000. She also wants to earn $20,000 per year from her investments, so 0.09x + 0.13y = 20,000. Solving these equations, we can find the values of x and y:

x + y = 200,000

0.09x + 0.13y = 20,000

Multiplying the second equation by 100 to eliminate decimals, we get:

9x + 13y = 2,000,000

Multiplying the first equation by 9 and subtracting it from the second equation eliminates x, giving us:

13y - 9x = 2,000,000 - 9(200,000) = 2,000,000 - 1,800,000 = 200,000

Now, we can solve this equation for y:

13y = 200,000

y = 200,000 / 13 = 15,385.84

Substituting the value of y back into the first equation, we can solve for x:

x + 15,385.84 = 200,000

x = 200,000 - 15,385.84 = 184,614.16

Therefore, she should invest approximately $184,614.16 in the safe fund and $15,385.84 in the riskier fund to earn $20,000 per year from her investments.

Answer 2

She is to invest $150,000 in the low risk found at 9%
She is to invest $50,000 in the high risk found at 13%
Let x = money invested at 9%
Let y = money invested at 13%
x+y = 200000
.09x + .13 y = 20000
since
x = 200000-y
then
.09(200000-y) +.13y = 20000
18000-.09y+.13y = 20000
.04 y = 20000
y = 50000
then
x = 200,000-50000 =150000