Finding the Doubling Time for Money

How long will it take for the money in an account that accrues interest at a rate of 3%, compounded continuously, to double?

Solution

To solve this problem we need to use the Continuous Compounding Formula.

$LaTeX: A=Pe^{rt}$ $A=Pe^{rt}$

In this case, A = The Amount = 2(Principal) = 2P, and r = The Interest Rate = 3% = 0.03.

$LaTeX: 2P=Pe^{0.03t}$ $2P=Pe^{0.03t}$

$LaTeX: 2=e^{0.03t}$ $2=e^{0.03t}$

$LaTeX: \ln2=\ln e^{0.03t}=0.03t$ $\ln2=\ln e^{0.03t}=0.03t$

$LaTeX: t=\frac{\ln2}{0.03}\approx23.10$ $t=\frac{\ln2}{0.03}\approx23.10$

It will take about 23 years for the amount to double.