Annuity Formula
An annuity formula is used to find the present and future value of an amount. An annuity is a fixed amount of income that is given annually or at regular intervals. An annuity is an agreement with an insurance company in which you make a lump sum payment (onetime big payment) or series of payments and, in return, receive a regular fixed income, beginning either immediately or after some predefined time in the future. The annuity formula is used to find the present and future value of an amount. The annuity formula is explained below along with solved examples.
What Is Annuity Formula?
The annuity formula for the present value of an annuity and the future value of an annuity is very helpful in calculating the value quickly and easily. The Annuity Formulas for future value, and present value are:

The future value of an annuity
FV = P×((1+r)^{n}−1) / r 
The present value of an annuity
PV = P×(1−(1+r)^{}^{n}) / r
where,
 P = Value of each payment
 r = Rate of interest per period in decimal
 n = Number of periods

Example 1: Dan was getting $100 for 5 years every year at an interest rate of 5%. Find the future value of this annuity at the end of 5 years? Calculate it by using annuity formula.
Solution
The future value
Given: r = 0.05, 5 years = 5 yearly payments, so n = 5, and P = $100
FV = P×((1+r)^{n}−1) / r
FV = $100 × ((1+0.05)^{5}−1) / 0.05
FV = 100 × 55.256
FV = $552.56
Answer: The future value of annuity after the end of 5 years is $552.56. 
Example 2: If the present value of the annuity is $20,000. Assuming a monthly interest rate of 0.5%, find the value of each payment after every month for 10 years. Calculate it by using the annuity formula.
Solution
To find: The value of each payment
Given:
r = 0.5% = 0.005
n = 10 years x 12 months = 120, and PV = $20,000
Using formula for present value
PV = P×(1−(1+r)^{}^{n}) / r
Or, P = PV × ( r / (1−(1+r)^{−n}))
P = $20,000 × (0.005 / (1−(1.005)^{−120}))
P = $20,000 × (0.005/ (1−0.54963))
P = $20,000 × 0.011...
P = $220
Answer: The value of each payment is $220.