Question

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?

Answer 1

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