18. The APR of Bessie's savings account is 6%, and interest is compounded monthly. If the principal in Bessie's savings account was $5600 for an entire year, what will be the balance of her account after all the interest is paid for the year?
18. The APR of Bessie's savings account is 6%, and interest is compounded monthly. If the principal in Bessie's savings account was $5600 for an entire year, what will be the balance of her account after all the interest is paid for the year?
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter13: Sequences And Series
Section13.FOM: Focus On Modeling: Modeling With Recursive Sequences
Problem 5P
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Transcribed Image Text:### Educational Problem Example
**Example Problem: APR and Compound Interest Calculation**
**Problem Statement:**
18. The APR of Bessie's savings account is 6%, and interest is compounded monthly. If the principal in Bessie's savings account was $5600 for an entire year, what will be the balance of her account after all the interest is paid for the year?
**Explanation:**
To solve this problem, we need to calculate the final balance of an account with monthly compounded interest. Here are the steps to solve this:
1. **Identify the given information:**
- Annual Percentage Rate (APR) = 6%
- Interest is compounded monthly.
- Principal amount (P) = $5600
- Number of periods per year (n) = 12 (since interest is compounded monthly)
2. **Convert the APR to a monthly interest rate:**
- Monthly interest rate (r) = APR/12 = 6%/12 = 0.5%
3. **Convert the percentage to a decimal for calculation purposes:**
- Monthly interest rate in decimal = 0.5/100 = 0.005
4. **Use the compound interest formula:**
- Compound Interest Formula: A = P(1 + r/n)^(nt)
5. **Plug in the values:**
- A = 5600(1 + 0.005)^(12)
- A = 5600(1.005)^(12)
6. **Calculate the result:**
- A ≈ 5600 * 1.061677812
7. **Final Principal Balance After One Year:**
- A ≈ $5945.40
So, the balance of Bessie's account after all the interest is paid for the year would be approximately $5945.40.
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