Present Value Calculator

Present value (PV) is the cornerstone of modern finance: it answers the question “how much is a future cash flow worth right now?” Whether you are valuing a bond, sizing a pension, pricing a lease, or deciding between two investment projects, every calculation reduces to discounting future money back to today’s terms. This calculator handles all six standard PV forms in one place — lump sum, ordinary annuity, annuity-due, growing annuity, perpetuity, and growing perpetuity — together with a period-by-period breakdown so you can see exactly how each payment contributes.

How it works

The central idea is the time value of money: a unit of currency available today can be invested to earn a return, so it is worth more than the same unit received in the future. The rate at which we convert future value to present value is the discount rate — your required rate of return, cost of capital, or opportunity cost.

Lump sum

The simplest case: a single payment FV received n periods from now.

PV = FV / (1 + r)^n

where r is the effective periodic rate. The calculator derives it from your annual rate using the EAR decomposition (1 + r_annual)^(1/periods_per_year) - 1 rather than simple division, which gives the correct rate consistent with how yields are quoted.

Ordinary annuity

A stream of equal payments PMT at the end of each period (mortgages, bond coupons):

PV = PMT * [1 - (1 + r)^(-n)] / r

This is mathematically the sum of n geometric terms, each discounted by one more period than the last.

Annuity-due

Equal payments at the start of each period (rent, insurance premiums). Every payment is discounted by one fewer period than in the ordinary-annuity case, so:

PV_due = PMT * [1 - (1 + r)^(-n)] / r * (1 + r)

Growing annuity

Payments that grow at a constant rate g per period for n periods (salary-linked pension, escalating rents). When r is not equal to g:

PV = PMT / (r - g) * [1 - ((1 + g) / (1 + r))^n]

When r equals g exactly, the formula simplifies to PMT * n / (1 + r).

Perpetuity and growing perpetuity

A perpetuity pays PMT forever. Because each payment is discounted more heavily, the infinite series converges:

PV = PMT / r

A growing perpetuity (the Gordon Growth Model used in equity valuation) adds a constant growth rate g:

PV = PMT / (r - g), valid only when r is greater than g.

Worked example

Suppose you are offered a savings plan that pays £500 per month for 20 years (ordinary annuity, monthly frequency). Your required annual return is 7%. What is that stream of payments worth today?

Effective monthly rate: (1 + 0.07)^(1/12) - 1 = 0.5654%

Number of periods n = 20 * 12 = 240

PV = 500 * [1 - (1.005654)^(-240)] / 0.005654 = £64,643

The total undiscounted cash flows are £500 * 240 = £120,000, so the time-value discount is roughly £55,357 — meaning you would pay no more than £64,643 today to receive those payments at a 7% hurdle rate.

All computations run in your browser — no figures are sent to a server or stored anywhere.