Final answer:
To find the annual rate of interest for an account compounding continuously that doubles $1000 in 12 years, we use the formula A = Pe^{rt}, where r is the annual interest rate. Solving for r, we find r ≈ ln(2) / 12, which is approximately 5.776%.
Step-by-step explanation:
To determine the annual rate of interest for an account where $1000 doubles in 12 years with continuous compounding, we use the formula for continuously compounded interest: A = Pert, where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, and t is the time in years. Since the money doubles, A is $2000, P is $1000, and t is 12. To find r, we rearrange the formula to rt = ln(A/P). We then compute:
r = ln(2) / 12
By using a calculator, the value of ln(2) is approximately 0.6931, and we divide this by 12 to find:
r ≈ 0.6931 / 12
r ≈ 0.05776
Thus, the annual interest rate when compounded continuously that would double the money in 12 years is approximately 5.776%.