Question 1204756: An investor has $50,000 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 5.22%, with equal amounts invested in short- and intermediate-term bonds.
Answer by ikleyn(52786)   (Show Source):
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An investor has $50,000 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 5.22%, with equal amounts
invested in short- and intermediate-term bonds.
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x dollars invested in short-term (4% annually);
x dollars invested in intermediate-term (5% annually);
the rest (50000-2x) dollars invested in long-term (6% annually).
Now write the total annual interest equation
0.04x + 0.05x + 0.06(50000-2x) = 0.0522*50000.
Simplify step by step and find x
0.04x + 0.05x - 0.06*(2x) = 0.0522*50000 - 0.06*50000
(0.04 + 0.05 - 0.12)x = -390
-0.03x = -390
x = 390/0.03 = 13,000.
ANSWER. Invest $13,000 in short-term; $13,000 in intermediate-term; the resr 50000-13000-13000 = 24000 in long-term.
CHACK. 0.04*13000 + 0.05*13000 + 0.06*24000 = 2610 dollars, total annual interest.
0.0522*50000 = 2610 dollars, the same amount. ! solved correctly !
Solved
using one single unknown and one single equation.
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