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):
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