Final answer:
To calculate the compound annual growth rate (CAGR) for growing $100 billion to $297.8 billion over 15 years and 165 days, use the CAGR formula with the future value, present value, and the total number of years including the additional days converted into a fraction of a year.
Step-by-step explanation:
The question asks to calculate the compound annual growth rate (CAGR) that would be required to grow an investment from $100 billion to $297.8 billion over a period of 15 years and 165 days. To do this, we can use the formula for CAGR which is:
CAGR = (FV/PV)⁽¹'ⁿ⁾⁻¹
Where FV is the future value ($297.8 billion), PV is the present value ($100 billion), and n is the number of years. Since the period includes an additional 165 days beyond 15 years, we convert it into a fraction of a year which is 165/365. Therefore, the total number of years (n) is 15 + 165/365.
Using these values in the CAGR formula, we get:
CAGR = ($297.8 billion / $100 billion)⁽¹'⁽¹⁵⁺¹⁶⁵'³⁶⁵⁾⁾⁻¹
This can be calculated to find the required rate of return to achieve the specified growth.