Compound Interest - Example - Saving Goal

Example

You have placed \$1000 in your savings account. The rate, 1%, is compounded annually.

Your goal is to wait until your account contains \$1500. You are solving the following equation for `t` $$ \begin{align*} 1000 \left( 1 + 0.01 \right)^t &= 1500 \\ \left( 1 + 0.01 \right)^t &= \frac{1500}{1000} \\ 1.01^t &= 1.5 \\ \ln \left( 1.01^t \right) = \ln \left( 1.5 \right) \\ t \ln \left( 1.01 \right) = \ln \left( 1.5 \right) \\ t = \frac{\ln \left( 1.5 \right)}{\ln \left( 1.01 \right)} \\ t \approx 40.75 \\ \end{align*} $$ So it will take at least 41 years to reach \$1500

Question