SOLUTION: Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term

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Question 1205201: Mark has $100,000 to invest. His financial consultant advises him to diversify his investment in three types of bonds: short-term, intermediate-term, and long-term. The short-term bonds pay 4%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6% simple interest per year. Mark wishes to realize a total annual income of 5.1%, with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?
short-term
intermediate-term
long-term
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52805)   (Show Source): You can put this solution on YOUR website!
.
Mark has $100,000 to invest. His financial consultant advises him to diversify his investment
in three types of bonds: short-term, intermediate-term, and long-term.
The short-term bonds pay 4%, the intermediate-term bonds pay 5%, and the long-term bonds pay 6%
simple interest per year. Mark wishes to realize a total annual income of 5.1%,
with equal amounts invested in short- and intermediate-term bonds. How much should he invest in each type of bond?
short-term
intermediate-term
long-term
~~~~~~~~~~~~~~~~~~~~~~ 

x = short term;

x = intermediate term;

(100,000-2x) = long term.


Write the total annual interest equation

    0.04x + 0.05x + 0.06*(100000-2x) = 0.051*100000.


Simplify this equation and find x

    0.04x + 0.05x - 0.06*(2x) + 6000 = 5100

          -0.03x                      = 5100 - 6000

          -0.03x                     =    -900

                x                     =  = 30000.


ANSWER.  $30,000 = short term;  $30,000 = intermediate term;  $100,000 - $30,000 - $30,000 = $40,000 = long term.

Solved.

Notice that three unknowns are found using one equation in one unknown.



Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
Assuming investment for 1 year

              SIMPLE INT. RATE     QUANTITY Inv.      INTEREST earned

SHORT             4%                      x            0.04x

INTERMED.         5%                      x            0.05x

LONG              6%                  100000-2x       0.06(100000-2x)
 
Total             5.1%                 100000

Total interest




Wanting effective rate 5.1%
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