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An ordinary annuity is a series of regular payments made at the end of the period.

The future value of ordinary is the future value of a stream of equal payments made at the end of the period.

It is calculated as follow:

$$FV=C\left[\frac{\left(1+\frac{i}{m}\right)^{n m}-1}{\frac{i}{m}}\right]$$


C is the period of cash flow or payments.

i is the annual interest rate expressed in percentage

m is the number of times compounding occurs yearly

n is the number of years

To better understand this formula, we take three examples

Example 1

Supposed that N1500 is deposited at the end of each year for the next 6 years in an account paying 8% per year compounded annually. How much will be in the account at the end of the 6th year?


Remember that,

$$FV=C\left[\frac{\left(1+\frac{i}{m}\right)^{n m}-1}{\frac{i}{m}}\right]$$

Here C=1500, m=1 because compounding occurs annually, i=0.08, n=6






Example 2

Find the future value of a 3-year annuity if the periodic payment is 1000 and the annuity earns 6% interest compounded semi-annually


Recall that 

$$FV=C\left[\frac{\left(1+\frac{i}{m}\right)^{n m}-1}{\frac{i}{m}}\right]$$


Note: m is 2 because there are only 2 6-month in a year.




Example 3

Kenny wishes to determine how much depositing N1500 at the end of the period will amount to in the next 3 years. If the interest rate is 12% compounded quarterly, how much will be in his account?



Note: m is 4 because a year is equivalent to 4 quarters.




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