Use the compound-interest formula to find the account balance A, where P is principal, r is interest rate, n is number of compounding periods per year, t is time, in years, and A is account balance. P compounded t r 1 $53,530 9-% 2 Quarterly C The account balance is approximately $ (Simplify your answer. Type an integer or decimal rounded to two decimal places as needed.) 1

FINANCIAL ACCOUNTING
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Author:Libby
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Chapter1: Financial Statements And Business Decisions
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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
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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