Modifying the CAGR Formula
An investment is rarely made on January 1st and then sold on December 31st. Consider an investor who wishes to calculate the CAGR of a ₹10,000 investment made on June 1, 2018, and sold for ₹16,897.14 on September 9, 2023. Before performing the CAGR calculation, the investor must first determine the fractional remaining of the holding period. In 2018, they held the title for 213 days, an entire year in 2019, 2020, 2021, and 2022, and 251 days in 2023. This investment was kept for 5.271 years, as determined by the following formula,
Year | No. of Days |
---|---|
2013 | 213 days |
2014 | 365 |
2015 | 365 |
2016 | 365 |
2017 | 365 |
2018 | 251 |
The investment was held for a total of 1,924 days. Divide the total number of days by 365 to get the number of years, which is [Tex]=\frac{1924}{365}=5.271 [/Tex]. The total number of years the investment was held can be entered into the denominator of the exponent within the CAGR formula as follows:
[Tex]Investment~CAGR=\frac{₹16897.15}{₹10,000}^{(\frac{1}{5.271})}-1\times100=10.46% [/Tex]