3. Capital One has a 1-year CD paying 2.40% APY. If the stated or nominal interest rate is compounded monthly, find the stated interest rate equivalent to 2.40% APY. Use algebraic methods. Round to the nearest hundredth of a percent. (Source: https://www.capitalone.com/bank/cds/online-cds/#id_cdratesterms)
3. Capital One has a 1-year CD paying 2.40% APY. If the stated or nominal interest rate is compounded monthly, find the stated interest rate equivalent to 2.40% APY. Use algebraic methods. Round to the nearest hundredth of a percent. (Source: https://www.capitalone.com/bank/cds/online-cds/#id_cdratesterms)
Chapter12: Sequences, Series And Binomial Theorem
Section12.3: Geometric Sequences And Series
Problem 12.59TI: New grandparents decide to invest 3200 per month in an annuity for their grandson, The account will...
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Question
![**Problem 5: Calculating the Stated Interest Rate for a Capital One CD**
Capital One offers a 1-year Certificate of Deposit (CD) with an Annual Percentage Yield (APY) of 2.40%. To determine the stated or nominal interest rate when this interest is compounded monthly, use algebraic methods to find the equivalent rate corresponding to a 2.40% APY. Ensure the result is rounded to the nearest hundredth of a percent.
**Solution Method:**
1. **APY Calculation Formula:**
\[
\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1
\]
Where:
- \( r \) is the stated annual interest rate.
- \( n \) is the number of compounding periods per year (monthly compounding means \( n = 12 \)).
2. **Rearrange the Formula:**
Solve for \( r \):
\[
1 + \text{APY} = \left(1 + \frac{r}{n}\right)^n
\]
\[
\left(1 + 0.024\right) = \left(1 + \frac{r}{12}\right)^{12}
\]
3. **Algebraic Solution:**
- Raise both sides to the power of \(\frac{1}{12}\).
- Subtract 1 from the result.
- Multiply the resultant value by \( n \) (12 in this case) to find \( r \).
4. **Rounding:**
- Finally, convert \( r \) to a percentage and round to the nearest hundredth of a percent.
**Source:**
For detailed terms and conditions, visit the Capital One CD terms page [here](https://www.capitalone.com/bank/cds/online-cds/#id_cdratesterms).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9ef355a-fb22-427b-b06e-27c19f3d746c%2F89ba87ee-24ae-4e82-8a82-2321b6a9f248%2F74gmoek_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5: Calculating the Stated Interest Rate for a Capital One CD**
Capital One offers a 1-year Certificate of Deposit (CD) with an Annual Percentage Yield (APY) of 2.40%. To determine the stated or nominal interest rate when this interest is compounded monthly, use algebraic methods to find the equivalent rate corresponding to a 2.40% APY. Ensure the result is rounded to the nearest hundredth of a percent.
**Solution Method:**
1. **APY Calculation Formula:**
\[
\text{APY} = \left(1 + \frac{r}{n}\right)^n - 1
\]
Where:
- \( r \) is the stated annual interest rate.
- \( n \) is the number of compounding periods per year (monthly compounding means \( n = 12 \)).
2. **Rearrange the Formula:**
Solve for \( r \):
\[
1 + \text{APY} = \left(1 + \frac{r}{n}\right)^n
\]
\[
\left(1 + 0.024\right) = \left(1 + \frac{r}{12}\right)^{12}
\]
3. **Algebraic Solution:**
- Raise both sides to the power of \(\frac{1}{12}\).
- Subtract 1 from the result.
- Multiply the resultant value by \( n \) (12 in this case) to find \( r \).
4. **Rounding:**
- Finally, convert \( r \) to a percentage and round to the nearest hundredth of a percent.
**Source:**
For detailed terms and conditions, visit the Capital One CD terms page [here](https://www.capitalone.com/bank/cds/online-cds/#id_cdratesterms).
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