Present Value of an Annuity

This formula gives the single lump sum that is equivalent to receiving the same payment at the end of each period for a fixed number of periods. It works by discounting each future payment back to today using the interest rate, then adding those discounted values together; the closed-form expression is just the sum of that geometric series. In actuarial work, it converts a stream of level payments into one present-day value so different cash-flow options can be compared fairly.

Use this when you need the current value of equal periodic payments, such as pensions, loan repayments, lease payments, or insurance settlement streams. It is appropriate when the payment amount, interest rate, and number of periods are all fixed and payments are made at the end of each period.

• Using the formula for payments made at the beginning of each period instead of the end
• Entering the interest rate as 5 instead of 0.05
• Forgetting that n counts the total number of payment periods, not years if payments are more frequent than yearly