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
Related questions
Question
![**Compound Interest Calculation:**
---
**Question 3:**
An investment of $100 compounded annually for two years at an interest rate of 3% would provide the investor with how much of a return?
**Options:**
A. $6.00
B. $100.00
C. $3.02
D. $6.09
To find out the amount of return from an investment of $100 compounded annually at an interest rate of 3% over two years, we can use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the future value of the investment/loan, including interest
- \( P \) = the principal investment amount (the initial amount of money)
- \( r \) = the annual interest rate (decimal)
- \( n \) = the number of times that interest is compounded per year
- \( t \) = the number of years the money is invested or borrowed for
Given:
- \( P = 100 \)
- \( r = 0.03 \)
- \( n = 1 \) (compounded annually)
- \( t = 2 \)
Plugging these values into the formula:
\[ A = 100 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 2} \]
\[ A = 100 \left(1 + 0.03\right)^2 \]
\[ A = 100 \left(1.03\right)^2 \]
\[ A = 100 \left(1.0609\right) \]
\[ A = 106.09 \]
The investor would receive $106.09 at the end of two years. Therefore, the amount of return on the investment is:
\[ 106.09 - 100 = 6.09 \]
Thus, the correct answer is option D: $6.09.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc57c022f-490d-46f8-85ed-7491dd14223c%2Fc7283a79-13d9-4362-9554-f6c1f99d5281%2F87n595o_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Compound Interest Calculation:**
---
**Question 3:**
An investment of $100 compounded annually for two years at an interest rate of 3% would provide the investor with how much of a return?
**Options:**
A. $6.00
B. $100.00
C. $3.02
D. $6.09
To find out the amount of return from an investment of $100 compounded annually at an interest rate of 3% over two years, we can use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) = the future value of the investment/loan, including interest
- \( P \) = the principal investment amount (the initial amount of money)
- \( r \) = the annual interest rate (decimal)
- \( n \) = the number of times that interest is compounded per year
- \( t \) = the number of years the money is invested or borrowed for
Given:
- \( P = 100 \)
- \( r = 0.03 \)
- \( n = 1 \) (compounded annually)
- \( t = 2 \)
Plugging these values into the formula:
\[ A = 100 \left(1 + \frac{0.03}{1}\right)^{1 \cdot 2} \]
\[ A = 100 \left(1 + 0.03\right)^2 \]
\[ A = 100 \left(1.03\right)^2 \]
\[ A = 100 \left(1.0609\right) \]
\[ A = 106.09 \]
The investor would receive $106.09 at the end of two years. Therefore, the amount of return on the investment is:
\[ 106.09 - 100 = 6.09 \]
Thus, the correct answer is option D: $6.09.
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