Final answer:
To determine the annual interest rate for a $2000 investment to grow to $4,000,000 in 200 years, the compound interest formula can be used to solve for the interest rate. By rearranging the formula, we can calculate the rate with the given figures from the question.
Step-by-step explanation:
The student's question asks about the interest rate required for an original $2000 to grow to $4,000,000 over a period of 200 years when compounded annually. To solve this, we can use the formula for compound interest, which is A = P(1 + r)^n 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), and n is the number of years the money is invested or borrowed for.
To find the interest rate (r), we rearrange the formula to solve for r: r = ((A/P)^(1/n)) - 1. Plugging in the values from the question, we get r = ((4,000,000/2,000)^(1/200)) - 1. Once we calculate this value, we will find the annual interest rate that would allow $2000 to grow to $4,000,000 in 200 years.