In this post, we will see two very simple, yet powerful shortcuts for calculating the Net Present Value (NPV) of a cash flow, though you may have learnt these formulas already, but they are very useful when finding the Net Present Value of a cash flow stream, especially for long cash flow streams spanning multiple periods.

**1. Sum of a geometric series from 0 to n (n +1 terms):**

Given a constant 'a' and a constant ratio 'r'

Example:

Consider a cash flow stream (40, 40, 40, 40) at an yearly interest rate 10%, the present value of this cash flow stream is given by

Through the above geometric series formula (with a = 40, r = 1/1.1 and n = 4), it's given by

Through the above geometric series formula (with a = 40, r = 1/1.1 and n = 4), it's given by

**2. Sum of a geometric series from 1 to n:**

Given a constant 'a' and a constant ratio 'r'

**Example:**

Consider a cash flow stream (-10, 40, 40, 40) at an yearly interest rate 10%, the present value of this cash flow stream is given by

Through the above geometric series formula, we get (add -10 to the sum of geometric series from 1 to n with a = 40, r = 1/1.1 and n = 3)

Thus, the sum of a geometric progression has a practical application when computing the Net Present Value of a cash flow stream.

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