Final answer:
To double a principal at an annual interest rate of 7% compounded continuously, we use the continuous compounding formula. After calculation, it would take approximately 10 years to double the principal.
Step-by-step explanation:
To determine how long it takes to double a principal amount at an annual interest rate of 7% compounded continuously, we can use the formula for continuous compounding, P = P0ert, where P is the future value, P0 is the initial principal, r is the annual interest rate, and t is the time in years. To double the principal, P is 2P0. We can express this as 2 = ert and solve for t.
Using the interest rate of 0.07 and setting up the equation 2 = e0.07t, we can take the natural logarithm (ln) of both sides to solve for t. After rearranging, the equation becomes t = ln(2)/0.07.
Calculating this gives us t ≈ 9.9 years, which we round up to the nearest whole number; therefore, the closest answer is 10 years.