What is the present value of an annuity formula?

PV = PMT x [1 - (1 + r)^(-n)] / r. Where PMT is the periodic payment, r is the interest rate per period, and n is the number of periods. For an annuity due (payments at start), multiply by (1 + r).

What is a growing annuity?

A growing annuity has payments that increase at a constant rate g each period. PV = PMT / (r - g) x [1 - ((1 + g)/(1 + r))^n]. If g = r the formula simplifies to PV = PMT x n / (1 + r).

What is a perpetuity?

A perpetuity pays a fixed amount forever. PV = PMT / r. A growing perpetuity: PV = PMT / (r - g). Used to value preferred stock, real estate income, and pension obligations in some actuarial contexts.

How is an annuity different from a lump sum?

A lump sum is a single payment. An annuity is a series of payments. The present value concept translates between them using the time value of money. Comparing a lump sum pension offer to an annuity requires this conversion.

What discount rate should I use?

For personal decisions: use a safe investment return you could earn (e.g., Treasury bond yield). For business decisions: use the cost of capital or WACC. For insurance annuities: the insurer uses a rate based on their investment portfolio.

Annuity Present Value and Payment Calculator

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Frequently Asked Questions

What is the present value of an annuity formula?

What is a growing annuity?

What is a perpetuity?

How is an annuity different from a lump sum?

What discount rate should I use?