Concept explainers
To find : the amount invested in 3.5% bond.
Answer to Problem 51E
The amount invested in 3.5% bond is
Explanation of Solution
Given information : Total amount invested in two corporate bonds that pay 3.5% and 5% simple interest is $24000. Annual interest income required for the investments is $930
Formula used:
Concept Involved:
Assign variable for the unknown that we need to find. Write system of equations based on the given statements. Solve the system of equation either by elimination method or by substitution method.
Calculation:
Description | Steps |
Assign variables for the unknown that we need to find | Let x be the amount invested in corporate bond paying 3.5% as interest, and y be the amount invested in corporate bond paying 5% as interest |
Write an equation based on total amount of investment. Amount invested in corporate bond paying 3.5% interest + Amount invested in corporate bond paying 5% interest = Total investment | |
Use the interest formula to find the interest amount earned due to the investment in corporate bond paying 3.5% interest in one year |
Calculation (Continued):
Description | Steps |
Use the interest formula to find the interest amount earned due to the investment in corporate bond paying 5% interest in one year | |
Write an equation based on the information that Annual interest income required for the investments is $930 | |
Label the system of equations | |
Solve the 1st equation for y by subtracting x on both sides | |
Substitute 24000 − x for y in the 2nd equation | |
Distribute 0.05 in the left side of the equation | |
Group and combine like terms | |
In the process of solving for x subtract 1200 on both sides of the equation and simplify | |
Dividing -0.015 on both sides and simplify fraction on both sides | |
Substitute 18000 for x in |
Conclusion:
The amount invested in corporate bond paying 3.5% as interest is $18000 and the amount invested in corporate bond paying 5% as interest is $6000
Chapter 7 Solutions
EBK PRECALCULUS W/LIMITS
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