Answer The amount invested in 3.5% bond is $ 18000 Explanation 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: I = P ⋅ r ⋅ t whereP represents the initial investment, r represents the annual rate of interest in decimal, t represents the number of years and I represent the simple interest. 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 x + y = 24000 Use the interest formula to find the interest amount earned due to the investment in corporate bond paying 3.5% interest in one year I 3.5 % = x ⋅ 0.035 ⋅ 1 = 0.035 x 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 I 5 % = y ⋅ 0.05 ⋅ 1 = 0.05 y Write an equation based on the information that Annual interest income required for the investments is $930 0.035 x + 0.05 y = 930 Label the system of equations x + y = 24000 → 1 s t E q u a t i o n 0.035 x + 0.05 y = 930 → 2 n d E q u a t i o n Solve the 1 s t equation for y by subtracting x on both sides x + y − x = 24000 − x y = 24000 − x Substitute 24000 − x for y in the 2 n d equation 0.035 x + 0.05 ( 24000 − x ) = 930 Distribute 0.05 in the left side of the equation 0.035 x + 0.05 ( 24000 ) + 0.05 ( − x ) = 930 0.035 x + 1200 − 0.05 x = 930 Group and combine like terms 0.035 x − 0.05 x + 1200 = 930 − 0.015 x + 1200 = 930 In the process of solving for x subtract 1200 on both sides of the equation and simplify − 0.015 x + 1200 − 1200 = 930 − 1200 − 0.015 x = − 270 Dividing -0.015 on both sides and simplify fraction on both sides − 0.015 x − 0.015 = − 270 − 0.015 x = 18000 Substitute 18000 for x in y = 24000 − x y = 24000 − 18000 = 6000 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

3rd Edition

ISBN: 9781133947202

Author: Ron Larson

Publisher: Cengage Learning

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Question

Chapter 7.2, Problem 51E

To determine

To find : the amount invested in 3.5% bond.

Expert Solution & Answer

Answer to Problem 51E

The amount invested in 3.5% bond is $18000

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:

I = P⋅r⋅t whereP represents the initial investment, r represents the annual rate of interest in decimal, t represents the number of years and I represent the simple interest.

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	x+y=24000
Use the interest formula to find the interest amount earned due to the investment in corporate bond paying 3.5% interest in one year	I3.5%=x⋅0.035⋅1 =0.035x

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	I5%=y⋅0.05⋅1 =0.05y
Write an equation based on the information that Annual interest income required for the investments is $930	0.035x+0.05y=930
Label the system of equations	x+y=24000→1st Equation0.035x+0.05y=930→2nd Equation
Solve the 1^s^t equation for y by subtracting x on both sides	x+y−x=24000−xy=24000−x
Substitute 24000 − x for y in the 2ⁿ^d equation	0.035x+0.05(24000−x)=930
Distribute 0.05 in the left side of the equation	0.035x+0.05(24000)+0.05(−x)=9300.035x+1200−0.05x=930
Group and combine like terms	0.035x−0.05x+1200=930−0.015x+1200=930
In the process of solving for x subtract 1200 on both sides of the equation and simplify	−0.015x+1200−1200=930−1200 −0.015x=−270
Dividing -0.015 on both sides and simplify fraction on both sides	−0.015x−0.015=−270−0.015 x=18000
Substitute 18000 for x in y=24000−x	y=24000−18000 =6000

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 7.2, Problem 50E

Chapter 7.2, Problem 52E

Chapter 7 Solutions

Precalculus with Limits

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