A certificate of deposit (CD) is an agreement between a bank and a saver in which the bank guarantees an interest rate and the saver commits to leaving his or her deposit in the account for an agreed-upon period of time. First National Bank offers 2-year CDs at 9.12% compounded daily, and Citywide Savings offers 2-year CDs at 9.13% compounded quarterly. Compute the annual yield for each institution and determine which is more advantageous for the consumer. (Round your answers to two decimal places.)
FNB:	r =

Incorrect: Your answer is incorrect.
%
CS:	r =

To determine which certificate of deposit (CD) is more advantageous, we need to compute the annual yield (also known as the **effective annual rate, EAR**) for both banks. The formula to compute the effective annual rate depends on the number of compounding periods.

### Formula for Effective Annual Rate (EAR):
\[
\text{EAR} = \left( 1 + \frac{r}{n} \right)^n - 1
\]
Where:
- \( r \) = nominal interest rate (expressed as a decimal)
- \( n \) = number of compounding periods per year

---

### For First National Bank (FNB):
- **Nominal interest rate**: \( r = 9.12\% = 0.0912 \)
- **Compounded daily**: \( n = 365 \)

\[
\text{EAR}_{\text{FNB}} = \left( 1 + \frac{0.0912}{365} \right)^{365} - 1
\]

### For Citywide Savings (CS):
- **Nominal interest rate**: \( r = 9.13\% = 0.0913 \)
- **Compounded quarterly**: \( n = 4 \)

\[
\text{EAR}_{\text{CS}} = \left( 1 + \frac{0.0913}{4} \right)^4 - 1
\]

Now, let's compute the values for both institutions.

I'll calculate this for you.The effective annual rates (EAR) for each institution are:

- **First National Bank (compounded daily)**: 9.55%
- **Citywide Savings (compounded quarterly)**: 9.45%

Therefore, **First National Bank** offers a slightly more advantageous CD with a higher annual yield.

Would you like further details or have any other questions? Here are five related questions to explore:

1. How would changing the compounding frequency affect the EAR?
2. What if the interest rates were compounded monthly instead of daily or quarterly?
3. How can you calculate the total value of an investment in a CD after two years?
4. What are the tax implications on interest earned from CDs?
5. How does inflation impact the real value of the interest earned on CDs?

**Tip:** Always compare the **effective annual rate (EAR)** when choosing between investment options with different compounding frequencies.

A certificate of deposit (CD) is an agreement between a bank and a saver in which the bank guarantees an interest rate and the saver commits to leaving his or her deposit in the account for an agreed-upon period of time. First National Bank offers 2-year CDs at 9.12% compounded daily, and Citywide Savings offers 2-year CDs at 9.13% compounded quarterly. Compute the annual yield for each institution and determine which is more advantageous for the consumer.

Discover how to calculate and compare the effective annual rate (EAR) for CDs offered by First National Bank and Citywide Savings. This problem demonstrates the importance of compounding frequency when comparing interest rates. Learn to use the EAR formula to determine which bank provides a better yield. Suitable for students in Grades 10-12.

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