FINANCIAL ACCOUNTING
10th Edition
ISBN: 9781259964947
Author: Libby
Publisher: MCG
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![**Compound Interest Calculation**
**Problem Statement:**
Use the compound interest formula to find the account balance \( A \), where \( P \) is the principal, \( r \) is the interest rate, \( n \) is the number of compounding periods per year, \( t \) is time in years, and \( A \) is the account balance.
**Given Parameters:**
| Principal ( \( P \) ) | Interest Rate ( \( r \) ) | Compounded ( \( n \) ) | Time ( \( t \) ) |
|-----------------------------|--------------------------------|-------------------------------|-----------------------------------|
| \$53,530 | \( \frac{9}{2} \% \) | Quarterly | \( \frac{1}{2} \) |
**Formula:**
\[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \]
**Explanation:**
The above table provides the specific values needed to calculate the account balance.
**Calculation Steps:**
1. **Convert the interest rate from percentage to decimal:**
\[ \frac{9}{2} \% = 0.045 \text{ per quarter} \]
2. **Identify the number of compounding periods per year:**
Since the interest is compounded quarterly, \( n = 4 \).
3. **Calculate the time duration in terms of years:**
Given \( t = \frac{1}{2} \).
4. **Substitute the values into the compound interest formula:**
\[ A = 53530 \left( 1 + \frac{0.045}{4} \right)^{4 \cdot 0.5} \]
5. **Simplify inside the parentheses first:**
\[ 1 + \frac{0.045}{4} = 1 + 0.01125 = 1.01125 \]
6. **Calculate the exponent value:**
\[ 4 \cdot 0.5 = 2 \]
7. **Perform the final calculation:**
\[ A = 53530 \times (1.01125)^2 \]
\[ A \approx 53530 \times 1.02256 \]
\[ A \approx 54769.69 \]
The account balance is approximately](https://content.bartleby.com/qna-images/question/a3230e3d-dd38-497e-8c1e-7c1c5570828c/087374cb-e7fe-4c21-80b3-c8ca05c3700d/h8g9us_processed.jpeg)
Transcribed Image Text:**Compound Interest Calculation**
**Problem Statement:**
Use the compound interest formula to find the account balance \( A \), where \( P \) is the principal, \( r \) is the interest rate, \( n \) is the number of compounding periods per year, \( t \) is time in years, and \( A \) is the account balance.
**Given Parameters:**
| Principal ( \( P \) ) | Interest Rate ( \( r \) ) | Compounded ( \( n \) ) | Time ( \( t \) ) |
|-----------------------------|--------------------------------|-------------------------------|-----------------------------------|
| \$53,530 | \( \frac{9}{2} \% \) | Quarterly | \( \frac{1}{2} \) |
**Formula:**
\[ A = P \left( 1 + \frac{r}{n} \right)^{nt} \]
**Explanation:**
The above table provides the specific values needed to calculate the account balance.
**Calculation Steps:**
1. **Convert the interest rate from percentage to decimal:**
\[ \frac{9}{2} \% = 0.045 \text{ per quarter} \]
2. **Identify the number of compounding periods per year:**
Since the interest is compounded quarterly, \( n = 4 \).
3. **Calculate the time duration in terms of years:**
Given \( t = \frac{1}{2} \).
4. **Substitute the values into the compound interest formula:**
\[ A = 53530 \left( 1 + \frac{0.045}{4} \right)^{4 \cdot 0.5} \]
5. **Simplify inside the parentheses first:**
\[ 1 + \frac{0.045}{4} = 1 + 0.01125 = 1.01125 \]
6. **Calculate the exponent value:**
\[ 4 \cdot 0.5 = 2 \]
7. **Perform the final calculation:**
\[ A = 53530 \times (1.01125)^2 \]
\[ A \approx 53530 \times 1.02256 \]
\[ A \approx 54769.69 \]
The account balance is approximately
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