Question

Alan deposited $300 in an account that pays 6% interest

compounded continuously. Approximately how long will it

take for Alan's money to triple?

(Use the formula A = Pe^rt where A is the accumulated amount, P is the initial amount, r is the annual rate of interest, and t is the elapsed time in years.)

A - 7.95 years

B - 11.55 years

C - 18.31 years

D - 23.10 years

Answer 1

It will take approximately 18.31 years for Alan's money to triple in an account that pays 6% interest compounded continuously.

Step-by-step explanation:

To determine how long it will take for Alan's money to triple, we can use the formula A = Pe^rt, where A is the accumulated amount, P is the initial amount, r is the annual rate of interest, and t is the elapsed time in years. In this case, Alan deposited $300, so P = 300, and the interest rate is 6% or 0.06. We want to find the time it takes for Alan's money to triple, so A = 3P = 3(300) = 900. Plugging these values into the formula, we have 900 = 300e^(0.06t).

To solve for t, we can divide both sides by 300 to get 3 = e^(0.06t). Next, we take the natural logarithm (ln) of both sides to eliminate the exponential. ln(3) = 0.06t. Finally, we divide both sides by 0.06 to solve for t. t = ln(3) / 0.06 ≈ 18.31 years.