https://file.aiquickdraw.com/mathbot/file/1726594255641u4gsre8i.jpg

The problem asks to compute the annual yield for two different two-year CDs, each offered by a different bank. The rates are:

- **First National Bank (FNB)**: 9.12% compounded daily.
- **Citywide Savings (CS)**: 9.13% compounded quarterly.

To calculate the annual yield, we'll use the formula for the **Effective Annual Rate (EAR)**:

\[
EAR = \left(1 + \frac{r}{n}\right)^n - 1
\]

Where:
- \(r\) = nominal interest rate (as a decimal),
- \(n\) = number of compounding periods per year.

### 1. For First National Bank (FNB):
- \(r = 9.12\% = 0.0912\)
- Daily compounding means \(n = 365\).

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

### 2. For Citywide Savings (CS):
- \(r = 9.13\% = 0.0913\)
- Quarterly compounding means \(n = 4\).

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

Let me calculate both of these for you.The effective annual rates (EAR) for the two banks are as follows:

1. **First National Bank (FNB)**: 9.55% (compounded daily)
2. **Citywide Savings (CS)**: 9.45% (compounded quarterly)

These represent the true annual yields for each CD based on their respective compounding frequencies.

Would you like further clarification or have any questions?

Here are some related questions to consider:
1. How does the compounding frequency affect the annual yield?
2. Why does FNB's daily compounding result in a higher yield than CS's quarterly compounding, even though the rates are close?
3. What is the difference between nominal interest rate and effective annual rate?
4. Can you apply this formula for other compounding frequencies, such as monthly or semi-annually?
5. How would the yields change if the term was longer than two years?

**Tip**: The more frequently interest is compounded, the higher the effective yield, even if the nominal rate is the same!

First National Bank offers two-year CDs at 9.12% compounded daily, and Citywide Savings offers two-year CDs at 9.13% compounded quarterly. Compute the annual yield for each institution. (Round your answers to two decimal places.)

Learn how to calculate the annual yield of CDs with daily and quarterly compounding. First National Bank offers 9.12% compounded daily, while Citywide Savings offers 9.13% compounded quarterly. This problem uses the formula for the Effective Annual Rate (EAR) and provides step-by-step calculations.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation