Chapter 2.1, Problem 2E

Savings with regular Deposits Suppose you deposit D dollars at the beginning of each month into an account that pays a monthly rate of r as a decimal. Then, the balance B of the account after t months is given by

$B=D\left(1+r\right)\left(\frac{{\left(1+r\right)}^t-1}{r}\right)\text{ dollars}\text{.}$

Suppose you deposit $150 at the beginning of each month into an account that pays a monthly rate of $r=0.005,$ which corresponds to an APR of 6%. How long does it take for the account balance to build to $2500? Report your answer to the nearest whole month.