Imagine you set aside $d$ dollars at the start of each month into a savings account that offers a monthly interest rate of $i$, where $i$ is the annual interest rate divided by $12$ (for example, if the annual rate is $3.6\%$, then $i=\frac{0.036}{12}=0.003$). After the first month, your savings include your initial deposit plus the next deposit with interest applied, totaling $d+d(1+i)$. Extending this pattern, the total amount in your account after $n$ months is $S_n=d+d(1+i)+d(1+i{)}^2+\cdots +d(1+i{)}^{n-1}$. Find the total amount in your savings account after $5$ years ($60$ months) if you deposit $\$300$ each month and the monthly interest rate is $0.15\%$.