Lesson: Geometric Series
In this lesson, we will learn how to derive the formula to calculate any geometric series and how to use it to solve real-world problems.
Sample Question Videos
Worksheet: 25 Questions • 2 Videos
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 month’s 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.
Sarah saves every month in a high-performing investment fund. The fund is guaranteed to pay annual interest, compounded monthly.
How much is Sarah guaranteed to have in her fund at the end of 2 years?
Nader saves every month in an account that pays an annual interest rate of compounded monthly.
How much will be in Nader’s account after 4 years of regular saving? Give your answer to the nearest cent.
If the interest was compounded quarterly, how much would be in the account after 4 years?