Kevin is evaluating several investment opportunities. In determining his required return, he is considering the interest on savings account which pays a quoted rate (APR) of 5% p.a, compounded monthly and an investment portfolio which pays an average return of 6% p.a compounded semiannually. Determine the appropriate required return should be used in evaluating Kevin's investment opportunities.

To determine Kevin's appropriate required return for evaluating investment opportunities, we need to compare the two options provided in terms of their effective annual rates (EAR). The EAR accounts for compounding, which makes it a more accurate measure of return than the nominal interest rate (APR).

### Step 1: Calculate the Effective Annual Rate (EAR) for both options.

#### Option 1: Savings account with an APR of 5% compounded monthly
We use the formula for EAR when compounding is involved:
\[
\text{EAR} = \left( 1 + \frac{i}{n} \right)^n - 1
\]
Where:
- \(i\) is the nominal interest rate (APR),
- \(n\) is the number of compounding periods per year.

For the savings account:
- \(i = 0.05\) (5% APR),
- \(n = 12\) (compounded monthly).

\[
\text{EAR} = \left( 1 + \frac{0.05}{12} \right)^{12} - 1
\]

#### Option 2: Investment portfolio with an APR of 6% compounded semiannually
Again, we use the EAR formula.

For the investment portfolio:
- \(i = 0.06\) (6% APR),
- \(n = 2\) (compounded semiannually).

\[
\text{EAR} = \left( 1 + \frac{0.06}{2} \right)^2 - 1
\]

### Step 2: Calculate both EARs

Let's calculate the EAR for both the savings account and the investment portfolio.# Variables for the calculations
APR_savings = 0.05  # 5% APR for savings account
compounding_savings = 12  # Monthly compounding for savings account

APR_investment = 0.06  # 6% APR for investment portfolio
compounding_investment = 2  # Semiannual compounding for investment portfolio

# EAR formula: (1 + i/n)^n - 1
EAR_savings = (1 + APR_savings / compounding_savings) ** compounding_savings - 1
EAR_investment = (1 + APR_investment / compounding_investment) ** compounding_investment - 1

EAR_savings, EAR_investmentThe effective annual rates (EAR) are as follows:

- **Savings account:** 5.12% (rounded from 5.116%)
- **Investment portfolio:** 6.09% (rounded from 6.09%)

### Appropriate Required Return:
Kevin should consider using the higher EAR as the required return to evaluate his investment opportunities since it reflects a more competitive return rate. Thus, **6.09%** would be the appropriate required return.

Let me know if you'd like more details or explanations!

Here are 5 related questions:
1. How does monthly compounding affect the final amount compared to yearly compounding?
2. What happens to the EAR if the APR increases while compounding frequency stays constant?
3. How can Kevin adjust his investments to maximize returns given varying compounding frequencies?
4. Why is EAR a better metric than APR for comparing investment opportunities?
5. How does inflation affect Kevin's real required return over time?

**Tip:** Always compare investment opportunities using the same metric, like EAR, to ensure an accurate comparison of potential returns.

Calculate the required return for investment opportunities by comparing the effective annual rates (EAR) of a savings account with 5% APR compounded monthly and an investment portfolio with 6% APR compounded semiannually. Learn how to use EAR to evaluate investment returns effectively.

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