Answer:
She should invest $90,000 in the safe fund and $30,000 in the riskier fund
Step-by-step explanation:
* Lets explain how to solve the problem
- A retired woman has $120,000 to investment
- She has two options:
# Save investment fund that has an annual yield of 9%
# Riskier fund that has a 13% annual yield
- She would like to earn $12,000 per year from her investments
* Assume that she invest $x in the safe fund and $y in the riskier fund
∵ The total investment is $120,000
∵ x represents the amount of money invested in the safe fund
∵ y represents the amount of money invested in the riskier fund
∴ x + y = 120,000 ⇒ (1)
∵ The interest I = Prt, where P is the invested amount , r is the
percentage of the interest per year in decimal , t is the time
∵ The interest of x amount is 9%
∴ I = x × 9/100 × 1 = 0.09 x
∴ The interest of y amount is 13%
∴ I = y × 13/100 × 1 = 0.13 u
∵ She would like to earn $12,000 per year from her investment
∴ 0.09 x + 0.13 y = 12,000 ⇒ (2)
* Lets solve the two equations to find x and y
- Multiply equation (1) by -0.13 to eliminate y
∵ -0.13 x + -0.13 y = -15600 ⇒(3)
- Add equations (2) and (3)
∴ (0.09 x + - 0.13 x) + (0.013 y + -0.13 y) = 12,000 + - 15,600
∴ -0.04 x = -3,600
- Divide both sides by -0.04
∴ x = 90,000
- Substitute the value of x in equation (1)
∴ 90,000 + y = 120,000
- Subtract 90,000 from both sides
∴ y = 30,000
∵ x represents the amount invested in the safe fund
∵ y represents the amount invested in the riskier fund
∴ She should invest $90,000 in the safe fund and $30,000 in
the riskier fund
