Word Problem

Question

An investor has $40,000 to invest in three types of bonds: short-term, intermediate-term, and long-term. How much should she invest in each type to satisfy the given conditions?

 

Short-term bonds pay 4% annually, intermediate-term bonds pay 5%, and long-term bonds pay 6%. The investor wishes to realize a total annual income of 4.95%, with equal amounts invested in short- and intermediate-term bonds.

 

short-term bonds=?

intermediate-term bonds=?

long-term bonds=?

 

 

Answer 1

Let x = amount invested in short-term bonds

          = amount invested in intermediate term bonds

      y = amount invested in long term bonds

 

Then, 0.04x + 0.05x + 0.06y = 0.0495(40000)

                  x + x + y = 40000

 

0.09x + 0.06y = 1980

     2x + y = 40000

 

From the second equation, y = 40000 - 2x

 

Replace y by 40000 - 2x in the first equation:

 

   0.09x + 0.06(40000 - 2x) = 1980

 

   0.09x + 2400 - 0.12x = 1980

 

                           -0.03x = -420

 

                                    x = 14000

 

Invest $14000 in short term bonds, $14000 in intermediate term bonds, and $12000 in long term bonds.