In order to pay for college, the parents of a child invest $15,000 in a bond that pays 7% interest compounded semiannually. How much money will there be in 21 years? Round your answer to the nearest cent. In 21 years the bond will be worth X
In order to pay for college, the parents of a child invest $15,000 in a bond that pays 7% interest compounded semiannually. How much money will there be in 21 years? Round your answer to the nearest cent. In 21 years the bond will be worth X
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![**Problem Statement:**
In order to pay for college, the parents of a child invest $15,000 in a bond that pays 7% interest compounded semiannually. How much money will there be in 21 years? Round your answer to the nearest cent.
**Answer Field:**
In 21 years the bond will be worth $ _______.
[Input field for the answer box with an "X" button for clearing the entry and a "↻" button for resetting the calculation]
**Detailed Explanation and Steps to Solve:**
To solve this problem, we need to use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
Given data:
- \( P = \$15,000 \)
- \( r = 7\% = 0.07 \)
- \( n = 2 \) (since interest is compounded semiannually)
- \( t = 21 \) years
Plugging in the values:
\[ A = 15000 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 21} \]
\[ A = 15000 \left(1 + 0.035\right)^{42} \]
\[ A = 15000 \left(1.035\right)^{42} \]
Using a calculator for precise computation:
\[ A \approx 15000 \times 4.242565 \]
\[ A \approx \$63,638.48 \]
Therefore, in 21 years the bond will be worth approximately \$63,638.48.
This transcribed and explained problem helps in understanding the application of compound interest to long-term investments.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf54cc92-fe70-42ec-a5a5-6c03b8447a69%2F6b0e9121-0a13-424a-81c7-84ac2ef7fc21%2Fr20jtmk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
In order to pay for college, the parents of a child invest $15,000 in a bond that pays 7% interest compounded semiannually. How much money will there be in 21 years? Round your answer to the nearest cent.
**Answer Field:**
In 21 years the bond will be worth $ _______.
[Input field for the answer box with an "X" button for clearing the entry and a "↻" button for resetting the calculation]
**Detailed Explanation and Steps to Solve:**
To solve this problem, we need to use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
Given data:
- \( P = \$15,000 \)
- \( r = 7\% = 0.07 \)
- \( n = 2 \) (since interest is compounded semiannually)
- \( t = 21 \) years
Plugging in the values:
\[ A = 15000 \left(1 + \frac{0.07}{2}\right)^{2 \cdot 21} \]
\[ A = 15000 \left(1 + 0.035\right)^{42} \]
\[ A = 15000 \left(1.035\right)^{42} \]
Using a calculator for precise computation:
\[ A \approx 15000 \times 4.242565 \]
\[ A \approx \$63,638.48 \]
Therefore, in 21 years the bond will be worth approximately \$63,638.48.
This transcribed and explained problem helps in understanding the application of compound interest to long-term investments.
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