A retired woman has $180,000 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 $18,000 per year from her investments?

Solution:

Let the amount invested in scheme which yields 9% be x and amount invested in scheme which yields 13% be y.

x + y = 180000 - - equation 1

0.09x + 0.13y = 18000 - - equation 2

Balancing the equations, multiply equation 1 with 0.09 and equation 2 with 1,

0.09x + 0.09y = 16200 - equation 3

0.09x + 0.13y = 18000 - - equation4

Subtracting equation 4 from 3,

-0.04y = - 1800

y = 45000

Now putting value of y in equation 1,

x + 45000 = 180000

x = 135000

The amount to be invested in scheme which yields 9% = $135,000

The amount to be invested in scheme which yields 13% = $45,000