Final answer:
To find the annual compound interest rate that results in a 37% growth over 11 years when compounded 380 times annually, one must use the compound interest formula, where 'A' represents the accumulated amount after 11 years (A = 1.37P), 'P' is the principal, 'r' is the annual rate, 'n' is the compound frequency, and 't' is the time in years. By rearranging the formula to solve for 'r', we can calculate the required interest rate.
Step-by-step explanation:
To calculate the annual compound interest rate required for an investment to grow by 37% over 11 years, with interest compounded 380 times per year, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
- A is the amount of money accumulated after n years, including interest.
- P is the principal amount (the initial amount of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
We know that A = P * 1.37, n = 380, and t = 11. To find r, we need to rearrange the formula:
r = (A/P)^(1/(nt)) - 1
and then we can calculate r by plugging in A/P = 1.37, n = 380, and t = 11.