On August 24, 1997 (which was the 236th day of that year), the Fidelity Select Electronics Fund reported a 44.3 percent return on investments for the year to date. Calculate an annual growth rate for this fund in 1997. Explain your method and the assumptions you made.
For the sake of your question, let us assume you started with $100. At the end of 236th day, your $100 was worth $144.30 .
1 - We will calculate the daily compound interest rate of growth over the period of 236 days as follows:
[144.30 / 100]^(1/236) =1.00155512 - 1 * 100 =0.155512 % - this is the daily compound interest rate.
2 - We will annualize this rate as follows: [1.00155512]^365 =1.7632867 - 1 * 100 =76.32867 % - this is the annual growth rate for this fund, compounded daily.