What is the formula for future value?

FV = PV(1 + r)^n + PMT × ((1 + r)^n − 1) ÷ r. The first term is the lump-sum growth; the second is the future value of recurring payments.

How do I convert an annual rate to a per-period rate?

Divide the annual rate by the number of periods per year. For monthly periods divide by 12; quarterly by 4; daily by 365. Then enter that value in the "rate per period" field.

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

Ordinary annuity payments occur at the END of each period; annuity-due payments occur at the START. Annuity-due earns one extra period of interest per payment, so its FV is the ordinary FV multiplied by (1 + r).

When the rate is zero, FV_annuity = PMT × n (no compounding). The calculator handles this case so it does not divide by zero.

Does this account for inflation or taxes?

No — it is a nominal, pre-tax projection. Use a real (inflation-adjusted) rate if you want real-terms output; deduct taxes separately.

Is the calculation private?

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

Future Value Calculator

Find the future value of a lump sum, an annuity stream, or both combined.

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 future value calculator

Enter the present value (PV) — the lump sum invested today. Leave 0 if you only have a payment stream.
Optionally enter a payment per period (PMT) for a recurring contribution.
Type the rate per period as a percent — for example, 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 future value, the lump-sum and annuity portions, and interest earned.

About this future value calculator

The future value calculator implements the two standard time-value-of-money formulas. Lump-sum future value: FV_lump = PV(1 + r)^n. Future value of an annuity: FV_annuity = PMT × ((1 + r)^n − 1) ÷ r; multiplying by (1 + r) converts this to an annuity-due if payments land at the start of each period. The combined FV = FV_lump + FV_annuity. These definitions match the CFA Institute Time-Value-of-Money curriculum and the U.S. SEC's Investor.gov "Future Value" primer.

Worked example: PV = USD 5,000, PMT = USD 100 at the end of each period, r = 0.5% per period (i.e. 6%/yr ÷ 12), n = 120 periods (10 years monthly). FV_lump = 5,000 × (1.005)^120 ≈ USD 9,096.98. FV_annuity = 100 × ((1.005)^120 − 1) ÷ 0.005 ≈ USD 16,387.93. Future value ≈ USD 25,484.91. Total invested = 5,000 + 100·120 = USD 17,000; interest earned ≈ USD 8,484.91. Currency is a label only; there is no exchange-rate lookup.

FAQ

What is the formula for future value?: FV = PV(1 + r)^n + PMT × ((1 + r)^n − 1) ÷ r. The first term is the lump-sum growth; the second is the future value of recurring payments.
How do I convert an annual rate to a per-period rate?: Divide the annual rate by the number of periods per year. For monthly periods divide by 12; quarterly by 4; daily by 365. Then enter that value in the "rate per period" field.
What is the difference between ordinary annuity and annuity-due?: Ordinary annuity payments occur at the END of each period; annuity-due payments occur at the START. Annuity-due earns one extra period of interest per payment, so its FV is the ordinary FV multiplied by (1 + r).
What if r = 0?: When the rate is zero, FV_annuity = PMT × n (no compounding). The calculator handles this case so it does not divide by zero.
Does this account for inflation or taxes?: No — it is a nominal, pre-tax projection. Use a real (inflation-adjusted) rate if you want real-terms output; deduct taxes separately.
Is the calculation private?: Yes. All math runs in your browser; nothing is sent to a server.