If $35000 is put in a savings account paying interest of 5% compounded annually, what amount will be in the account at the end of 6 years? O $45500 O $27878 O $46120 O $46904
If $35000 is put in a savings account paying interest of 5% compounded annually, what amount will be in the account at the end of 6 years? O $45500 O $27878 O $46120 O $46904
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
Problem 1Q
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![### Compound Interest Calculation
**Question:**
If $35,000 is put in a savings account paying interest of 5% compounded annually, what amount will be in the account at the end of 6 years?
**Options:**
1. $45,500
2. $27,878
3. $46,120
4. $46,904
### Explanation
Compound interest is calculated using the formula:
\[ A = P(1 + \frac{r}{n})^{nt} \]
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:
- \( P = 35,000 \)
- \( r = 5\% \) or \( 0.05 \)
- \( n = 1 \) (since the interest is compounded annually)
- \( t = 6 \) years
Plugging in these values:
\[ A = 35000 \left(1 + \frac{0.05}{1}\right)^{1 \times 6} \]
\[ A = 35000 (1 + 0.05)^6 \]
\[ A = 35000 (1.05)^6 \]
Using a calculator to compute \( (1.05)^6 \):
\[ (1.05)^6 \approx 1.3401 \]
Then,
\[ A \approx 35000 \times 1.3401 \]
\[ A \approx 46,904 \]
Thus, the correct answer is:
- \(\circ\) $46,904](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe2e52231-be4b-497d-891a-4dab4019ab2b%2F5d29962c-7ca6-4204-bf97-9fe4dcbaa4cc%2F7ctk23_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Compound Interest Calculation
**Question:**
If $35,000 is put in a savings account paying interest of 5% compounded annually, what amount will be in the account at the end of 6 years?
**Options:**
1. $45,500
2. $27,878
3. $46,120
4. $46,904
### Explanation
Compound interest is calculated using the formula:
\[ A = P(1 + \frac{r}{n})^{nt} \]
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:
- \( P = 35,000 \)
- \( r = 5\% \) or \( 0.05 \)
- \( n = 1 \) (since the interest is compounded annually)
- \( t = 6 \) years
Plugging in these values:
\[ A = 35000 \left(1 + \frac{0.05}{1}\right)^{1 \times 6} \]
\[ A = 35000 (1 + 0.05)^6 \]
\[ A = 35000 (1.05)^6 \]
Using a calculator to compute \( (1.05)^6 \):
\[ (1.05)^6 \approx 1.3401 \]
Then,
\[ A \approx 35000 \times 1.3401 \]
\[ A \approx 46,904 \]
Thus, the correct answer is:
- \(\circ\) $46,904
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