You put $1000 in an investment that earns 5% per year. How much will you have in 20 years? $2653.30 $14,462.55 $100,000 $3,325,257
You put $1000 in an investment that earns 5% per year. How much will you have in 20 years? $2653.30 $14,462.55 $100,000 $3,325,257
Chapter1: Understanding Personal Finance
Section: Chapter Questions
Problem 9DTM
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Question
![## Investment Growth Problem
### Question 7:
You put $1000 in an investment that earns 5% per year. How much will you have in 20 years?
### Options:
1. $2653.30
2. $14,462.55
3. $100,000
4. $3,325,257
### Explanation:
To solve this problem, you 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, which is $1000 in this case).
- \( r \) 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.
For this problem:
- \( P = 1000 \) dollars
- \( r = 0.05 \) (5% annual interest)
- \( n = 1 \) (compounded annually)
- \( t = 20 \) years
Plugging these values into the formula, we get:
\[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 20} \]
\[ A = 1000 (1.05)^{20} \]
\[ A \approx 1000 (2.6533) \]
\[ A \approx 2653.30 \]
Thus, the correct answer is \( $2653.30 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41cc9bd4-14af-44e6-b895-a9cd3485fa4c%2F5dea59a4-3fee-41e3-89de-ba099de54aee%2Fiq404n_processed.png&w=3840&q=75)
Transcribed Image Text:## Investment Growth Problem
### Question 7:
You put $1000 in an investment that earns 5% per year. How much will you have in 20 years?
### Options:
1. $2653.30
2. $14,462.55
3. $100,000
4. $3,325,257
### Explanation:
To solve this problem, you 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, which is $1000 in this case).
- \( r \) 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.
For this problem:
- \( P = 1000 \) dollars
- \( r = 0.05 \) (5% annual interest)
- \( n = 1 \) (compounded annually)
- \( t = 20 \) years
Plugging these values into the formula, we get:
\[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \cdot 20} \]
\[ A = 1000 (1.05)^{20} \]
\[ A \approx 1000 (2.6533) \]
\[ A \approx 2653.30 \]
Thus, the correct answer is \( $2653.30 \).
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