What is the formula for present value?

PV = FV ÷ (1 + r)^n + PMT × (1 − (1 + r)^−n) ÷ r. The first term discounts a future lump sum; the second is the present value of an annuity.

How do I pick the discount rate?

Use your opportunity cost of capital: the return you could earn elsewhere at comparable risk. Common picks are a risk-free rate (e.g. a Treasury yield), a corporate cost of capital, or a target hurdle rate. Divide annual figures by periods-per-year to get the per-period rate.

When is PV smaller than FV?

Whenever the discount rate is positive, PV < FV. A higher rate or longer horizon discounts the future amount more aggressively, pushing PV further below FV.

What is the difference between ordinary annuity and annuity-due?

Ordinary annuity payments occur at the END of each period; annuity-due at the START. Annuity-due cash flows arrive sooner, so their PV is higher by a factor of (1 + r).

When the discount rate is zero, PV_lump = FV and PV_annuity = PMT × n. The calculator handles this edge case so it does not divide by zero.

Is the calculation private?

Yes. All math runs in your browser; nothing is sent to a server.

Present Value Calculator

Q: What is the difference between ordinary annuity and annuity-due?

Ordinary annuity payments occur at the END of each period; annuity-due at the START. Annuity-due cash flows arrive sooner, so their PV is higher by a factor of (1 + r).

Q: What if r = 0?

When the discount rate is zero, PV_lump = FV and PV_annuity = PMT × n. The calculator handles this edge case so it does not divide by zero.

Q: Is the calculation private?

Yes. All math runs in your browser; nothing is sent to a server.

Discount a future amount and/or annuity payments back to a present value at any rate.

Written by Golam Rabbani, Founder & Lead Engineer

This interactive tool requires JavaScript. Read the formula and worked example below; you can compute the result by hand.

How to use this present value calculator

Enter the future value (FV) — the lump sum expected at the end of the horizon. Leave 0 if you only have a payment stream.
Optionally enter the payment per period (PMT) for a recurring cash flow.
Type the discount rate per period as a percent — divide an annual rate by 12 for monthly periods.
Type the number of periods (n).
Pick payment timing: end of period (ordinary annuity) or start (annuity-due).
Press Calculate to see the combined present value plus the lump-sum and annuity components.

About this present value calculator

Present value is what a future amount is worth today after discounting at a given rate. The calculator uses the two textbook formulas. Lump-sum present value: PV_lump = FV ÷ (1 + r)^n. Present value of an annuity: PV_annuity = PMT × (1 − (1 + r)^−n) ÷ r; multiply by (1 + r) for annuity-due. The combined PV = PV_lump + PV_annuity. These are the formulas in the CFA Institute Time-Value-of-Money curriculum and the U.S. SEC's Investor.gov "Present Value" primer.

Worked example: FV = USD 20,000 due in 60 months, PMT = USD 500 at the end of each month, discount rate r = 0.5% per month. PV_lump = 20,000 ÷ (1.005)^60 ≈ USD 14,827.92. PV_annuity = 500 × (1 − (1.005)^−60) ÷ 0.005 ≈ USD 25,861.93. Combined PV ≈ USD 40,689.85. That is the amount you should be willing to pay today for the right to receive USD 20,000 in 60 months plus USD 500 per month over that period, given a 0.5%/month discount rate. Currency is a label only; there is no exchange-rate lookup.

FAQ

What is the formula for present value?: PV = FV ÷ (1 + r)^n + PMT × (1 − (1 + r)^−n) ÷ r. The first term discounts a future lump sum; the second is the present value of an annuity.
How do I pick the discount rate?: Use your opportunity cost of capital: the return you could earn elsewhere at comparable risk. Common picks are a risk-free rate (e.g. a Treasury yield), a corporate cost of capital, or a target hurdle rate. Divide annual figures by periods-per-year to get the per-period rate.
When is PV smaller than FV?: Whenever the discount rate is positive, PV < FV. A higher rate or longer horizon discounts the future amount more aggressively, pushing PV further below FV.
What is the difference between ordinary annuity and annuity-due?: Ordinary annuity payments occur at the END of each period; annuity-due at the START. Annuity-due cash flows arrive sooner, so their PV is higher by a factor of (1 + r).
What if r = 0?: When the discount rate is zero, PV_lump = FV and PV_annuity = PMT × n. The calculator handles this edge case so it does not divide by zero.
Is the calculation private?: Yes. All math runs in your browser; nothing is sent to a server.