Linear Systems

Question

Mr. Hamilton has $50,000 to invest in a tax-free fund and in a money market fund. The tax-free fund pays 7.4% and the money market pays 8.8%. How much should he invest in each to get a return of $4,071 per year?

Answer 1

Let X be the amount invested in the tax-free fund and Y be the amount invested in the money market.

 

Note that 7.4% = 0.074 and 8.8% = 0.088

 

X + Y = 50000   -->  Y = 5000 - X

 

0.074X +  0.088Y = 4071

 

 

0.074X + 0.088( 50000 - X) = 4071

 

0.074X + 4400  - 0.088X  = 4071

 

 -0.014X = -329

 

X = 23500 --> Y = 50000 - 23500 = 26500

 

Check:   0.074 x 23500 +  0.088 x 26500 = 4071