**Q1: **

To calculate the amount of money in a structured savings account, where a saver deposits
a regular amount at regular time intervals, we consider each monthβs deposit separately.

Consider a saver who makes a regular deposit on the last day of every month in an account
where the interest is calculated on the last day of every month.

Let the regular deposit be , and let the monthly interest rate be (an interest rate of would give an value of ).

On the day the th deposit is made, the first deposit has been earning interest for
months, so its value is .

Similarly, on the day the th deposit is made, the second deposit has been earning
interest for months, so its value is .

The pattern continues until we consider the th deposit which has earned no interest on
the day it is deposited so its value is .

To calculate the total amount in the fund, , on the day the th deposit is made, we need
to find the sum of the values of the individual deposits.

Starting with the th deposit, we get

What kind of series do you see on the right-hand side of the equation?

Using the formula for the sum of the first terms of a geometric series, write a
formula for , the total amount in the fund.