The returns from an investment are 1% in Year 1, 4% in Year 2, and 14.8% in the first half of Year 3. Calculate the annualized return for the entire period.

Note: Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.

To calculate the annualized return, we first need to compute the overall return over the entire period. The formula for the total cumulative return over a multi-period investment is:

\[
(1 + r_{\text{total}}) = (1 + r_1) \times (1 + r_2) \times (1 + r_3)
\]

where:

- \( r_1 = 1\% = 0.01 \)
- \( r_2 = 4\% = 0.04 \)
- \( r_3 = 14.8\% = 0.148 \) (for the first half of Year 3)

### Step 1: Calculate the total cumulative return over the 2.5-year period
We can calculate this by multiplying the returns for each period:

\[
(1 + r_{\text{total}}) = (1 + 0.01) \times (1 + 0.04) \times (1 + 0.148)
\]

Let's compute this.The total return factor over the 2.5-year period is approximately 1.2059, which means the investment grew by about 20.59% over this time.

### Step 2: Calculate the annualized return
The formula for the annualized return \( r_{\text{annualized}} \) over \( n \) years is:

\[
r_{\text{annualized}} = (1 + r_{\text{total}})^{\frac{1}{n}} - 1
\]

Here, \( n = 2.5 \) years, and we already have \( (1 + r_{\text{total}}) = 1.2059 \).

Let's compute the annualized return.The annualized return over the 2.5-year period is approximately **7.78%**.

Would you like further clarification or more details?

Here are 5 related questions to explore:
1. How would the annualized return change if Year 3 had a return for the full year instead of just half?
2. How does compounding affect long-term investment returns?
3. What is the difference between simple and compound interest returns?
4. How can one calculate the return when some years have losses instead of gains?
5. What is the significance of annualizing returns for comparing different investments?

**Tip:** When dealing with investment returns over multiple periods, always remember to use compound growth, not simple addition of percentages!

The returns from an investment are 1% in Year 1, 4% in Year 2, and 14.8% in the first half of Year 3. Calculate the annualized return for the entire period. Note: Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.

Learn how to calculate the annualized return for an investment that earned 1% in Year 1, 4% in Year 2, and 14.8% in the first half of Year 3. This detailed step-by-step solution explains the key concepts of compound interest and investment growth, with a final annualized return of 7.78%.

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