Chapter 10.3, Problem 16E

Periodic savings Suppose you deposit m dollars at the beginning of every month in a savings account that earns a monthly interest rate of r, which is the annual interest rate d vided by 12 (for example, if tine annual interest rate is 2.4%, r − 0.024/12 − 0.002). For an initial investment of m dollars, the amount of money in your account at the beginning of the second month is the sum of your second deposit and your initial deposit plus interest, or m | m(l | r). Continuing in this fashion, it can be shown that tie amount of money in your account after n months is A_n m + m(1 + r) + ⋯ + m( 1 + r)ⁿ . Use geometric sums to determine the amount of money in your savings account after 5 years (60 months) using the given monthly deposit and interest rate.

16. Monthly deposits of $100 at an annual interest rate of 1 8%