What is an annuity?

An annuity is a series of payments made at equal intervals.

In the real world, for example, it can be understood as regular deposits to a savings account.

As you can find on Wikipedia here is the ordinary annuity formula:

Where

• PV: The present value of an ordinary annuity
• PMT: Value of each payment
• r: interest rate per period
• n: number of periods

And in Python?

If we literally transpose this formula in Python.

def compute_annuity_pv(pmt, r, n):
    """Compute the present value of an annuity"""
    return pmt * ((1 - (1/(1+r)**n)) / r)

If we take an example with

• PMT = 100$ : Value at each payment
• r = 7% or 0.07 : interest rate per period here 7% per annum.
• n = 5 : 5 years

print(compute_annuity_pv(100, 0.07, 5))
# 410.019

Here you are! You now know how to compute the present value of an annuity.

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