A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much is invested in each if the annual income from both bonds is $1980?
A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much is invested in each if the annual income from both bonds is $1980?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Problem: Investment in Two Bonds**
A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much is invested in each if the annual income from both bonds is $1,980?
**Solution Approach:**
To solve this problem, we need to use the concept of interest and solve it mathematically using a system of equations.
**Step 1: Define Variables**
Let:
- \( x \) be the amount invested in the bond with a 6% yield.
- \( y \) be the amount invested in the bond with a 12% yield.
**Step 2: Set Up Equations**
1. The total investment equation:
\[
x + y = 24,000
\]
2. The total income equation (using the yield percentages):
\[
0.06x + 0.12y = 1,980
\]
**Step 3: Solving the System of Equations**
To find the values of \( x \) and \( y \), solve the system of equations using substitution or elimination methods.
This can be solved by substituting known values or by manipulating the equations to find the exact distribution between the bonds.
**Conclusion:**
Solving these equations will provide the amounts invested in each bond. This approach illustrates how to apply algebraic methods to solve real-world financial problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9affadff-1dbc-4796-87cc-cd8c2c6f7c45%2F704c3990-00aa-4647-b5e7-dd782145b318%2Ff6kgox_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Investment in Two Bonds**
A physician invests $24,000 in two bonds. If one bond yields 6% and the other yields 12%, how much is invested in each if the annual income from both bonds is $1,980?
**Solution Approach:**
To solve this problem, we need to use the concept of interest and solve it mathematically using a system of equations.
**Step 1: Define Variables**
Let:
- \( x \) be the amount invested in the bond with a 6% yield.
- \( y \) be the amount invested in the bond with a 12% yield.
**Step 2: Set Up Equations**
1. The total investment equation:
\[
x + y = 24,000
\]
2. The total income equation (using the yield percentages):
\[
0.06x + 0.12y = 1,980
\]
**Step 3: Solving the System of Equations**
To find the values of \( x \) and \( y \), solve the system of equations using substitution or elimination methods.
This can be solved by substituting known values or by manipulating the equations to find the exact distribution between the bonds.
**Conclusion:**
Solving these equations will provide the amounts invested in each bond. This approach illustrates how to apply algebraic methods to solve real-world financial problems.
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