The returns from an investment are 2% in Year 1, 7% in Year 2, and 9.8% in the first half of Year 3. Calculate the annualized return for the entire period. (Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

Answer 1

To calculate the annualized return, we need to sum up the returns from each year and then find the compound annual growth rate (CAGR).

The returns from each year are as follows:
Year 1: 2%
Year 2: 7%
First half of Year 3: 9.8%

To find the compound annual growth rate, we use the formula:
CAGR = (Ending Value ÷ Beginning Value) ^ (1 ÷ Number of Years) - 1

We can assume that the initial investment is $100.

For Year 1, the return is 2% of $100, which is $2. So the Ending Value is $100 + $2 = $102.

For Year 2, the return is 7% of $102, which is $7.14. So the Ending Value is $102 + $7.14 = $109.14.

For the first half of Year 3, the return is 9.8% of $109.14, which is $10.68. So the Ending Value is $109.14 + $10.68 = $119.82.

Using the compound annual growth rate formula:
CAGR = ($119.82 ÷ $100) ^ (1 ÷ 2.5) - 1

Calculating the values inside the parenthesis:
CAGR = 1.1982 ^ (1 ÷ 2.5) - 1

CAGR = 1.1982 ^ 0.4 - 1

CAGR = 1.0837 - 1

CAGR = 0.0837

Converting to a percentage by multiplying by 100:
CAGR = 0.0837 * 100

CAGR = 8.37%

Therefore, the annualized return for the entire period is 8.37%.