was $525, how much mo 10. Nick, an attorney, divided his $15,000 bonus check among three different investments. He purchased a municipal bond paying 5.5% simple interest. He invested twice the amount of money that he paid for the municipal bonds in a certificate of deposit paying 4.5% simple interest. Nick placed the balance of the money in a money market account paying 3.75% simple interest. If Nick's total interest for the year was $692.50, how much was placed in each account?
was $525, how much mo 10. Nick, an attorney, divided his $15,000 bonus check among three different investments. He purchased a municipal bond paying 5.5% simple interest. He invested twice the amount of money that he paid for the municipal bonds in a certificate of deposit paying 4.5% simple interest. Nick placed the balance of the money in a money market account paying 3.75% simple interest. If Nick's total interest for the year was $692.50, how much was placed in each account?
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 10: Investment Allocation**
Nick, an attorney, divided his $15,000 bonus check among three different investments. He purchased a municipal bond that pays 5.5% simple interest. He invested twice the amount of money that he paid for the municipal bonds in a certificate of deposit paying 4.5% simple interest. Nick placed the balance of the money in a money market account paying 3.75% simple interest. If Nick's total interest for the year was $692.50, how much was placed in each account?
**Solution Strategy:**
- **Variables:**
- Let \( x \) be the amount invested in the municipal bonds.
- \( 2x \) will be the amount invested in the certificate of deposit.
- The balance, or \( 15,000 - x - 2x = 15,000 - 3x \), will be the amount in the money market account.
- **Interest Equations:**
- Interest from municipal bonds: \( 0.055x \)
- Interest from certificate of deposit: \( 0.045(2x) = 0.09x \)
- Interest from money market account: \( 0.0375(15,000 - 3x) \)
- **Total Interest:**
- Setting up the equation for total interest:
\[
0.055x + 0.09x + 0.0375(15,000 - 3x) = 692.50
\]
- **Solve for \( x \):**
- Simplify and solve the equation to find \( x \), then use \( x \) to find the amounts in each account.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9affadff-1dbc-4796-87cc-cd8c2c6f7c45%2F97773384-4adf-44fc-b7f3-0a375a314d26%2Fhhwmilt_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 10: Investment Allocation**
Nick, an attorney, divided his $15,000 bonus check among three different investments. He purchased a municipal bond that pays 5.5% simple interest. He invested twice the amount of money that he paid for the municipal bonds in a certificate of deposit paying 4.5% simple interest. Nick placed the balance of the money in a money market account paying 3.75% simple interest. If Nick's total interest for the year was $692.50, how much was placed in each account?
**Solution Strategy:**
- **Variables:**
- Let \( x \) be the amount invested in the municipal bonds.
- \( 2x \) will be the amount invested in the certificate of deposit.
- The balance, or \( 15,000 - x - 2x = 15,000 - 3x \), will be the amount in the money market account.
- **Interest Equations:**
- Interest from municipal bonds: \( 0.055x \)
- Interest from certificate of deposit: \( 0.045(2x) = 0.09x \)
- Interest from money market account: \( 0.0375(15,000 - 3x) \)
- **Total Interest:**
- Setting up the equation for total interest:
\[
0.055x + 0.09x + 0.0375(15,000 - 3x) = 692.50
\]
- **Solve for \( x \):**
- Simplify and solve the equation to find \( x \), then use \( x \) to find the amounts in each account.
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