Present Value Calculator
Discount a future lump sum and a stream of regular payments back to today's money at any nominal annual rate, term, and compounding frequency — the textbook time-value-of-money formula behind Excel's PV() function.
Present value
£30,937.12
- PV of future lump sum
- £3,020.96
- PV of payment stream
- £27,916.15
- Total nominal cash flows
- £58,000.00
- Time-value discount
- £27,062.88
Present value discounts future cash flows back to today using rate r: PV = FV/(1+r)^n + PMT · (1 − (1+r)^-n)/r · (1 + r·t). With end-of-period payments t=0 (Excel type=0); with beginning-of-period payments t=1 (Excel type=1) — annuity-due payments are worth slightly more because they arrive one period sooner.
How to use this calculator
Enter the future lump sum you expect to receive, any regular payment you will also receive each period, the annual discount rate, and the number of years. Choose how often payments and discounting occur, and whether payments arrive at the beginning or end of each period. The present value updates as you type.
How the calculation works
The calculator uses the standard time-value-of-money formula: PV = FV / (1+r)^n + PMT · (1 − (1+r)^-n) / r · (1 + r·t). Here r is the period rate (annual rate divided by periods per year), n is the total number of periods, and t is 0 for end-of-period payments (ordinary annuity, Excel type=0) or 1 for beginning-of-period payments (annuity due, Excel type=1). Setting PMT = 0 reduces it to the lump-sum case PV = FV / (1+r)^n; setting FV = 0 reduces it to the pure annuity case.
Worked example
Example: $10,000 to be received in 20 years plus $200 received each month over that period at a 6% nominal annual discount rate (monthly), end-of-period payments. Period rate r = 0.005, periods n = 240. PV of lump sum = 10,000 / 1.005^240 ≈ $3,020.96. PV of payments = 200 · (1 − 1.005^-240) / 0.005 ≈ $27,916.15. Total PV ≈ $30,937.12 against $58,000 of nominal cash flows — roughly $27,063 of value is lost to discounting. Switching to beginning-of-period payments multiplies the payments portion by (1 + r), raising PV to about $31,076.70.
Frequently asked questions
What is present value in finance?
Present value is the amount of money you would need today, invested at a stated rate of return, to grow into a specified future cash flow over a specified number of periods. It is the time-value-of-money mirror image of future value: future value compounds today's money forward, present value discounts tomorrow's money back. The same maths is used to price bonds, value annuities and pensions, evaluate capital-budgeting projects (NPV), and compare lump-sum versus instalment offers.
How do I choose the right discount rate?
The discount rate represents the return you could earn on the money if you had it today — your opportunity cost of capital. For a low-risk corporate cash flow, many analysts use the yield on a comparable-maturity government bond plus a small spread. For a riskier project, the weighted average cost of capital (WACC) is the standard textbook choice. For personal finance — comparing a lump-sum lottery payout to an annuity, for example — your own expected long-run return on diversified investments is reasonable. Higher rate = lower present value, so the choice matters.
What is the difference between end-of-period and beginning-of-period payments?
End-of-period (ordinary annuity) payments arrive at the close of each period — typical for loan repayments, bond coupons, and most savings plans. Beginning-of-period (annuity due) payments arrive at the start of each period — typical for rents, leases, and some pension payouts. Each beginning-of-period payment is discounted by one fewer period, so for the same rate, term, and payment amount, the present value of an annuity due is exactly (1 + r) times the present value of an ordinary annuity, where r is the period rate.
Does this match Excel's PV() function?
Yes. Excel =PV(rate, nper, pmt, fv, type) returns the present value of a TVM stream with the opposite sign convention (positive pmt and fv are treated as inflows, so PV comes out negative). This calculator shows the absolute value. So =PV(0.06/12, 240, 200, 10000, 0) ≈ -30,937.12 matches the worked example with end-of-period payments. With type=1 (beginning-of-period), =PV(0.06/12, 240, 200, 10000, 1) ≈ -31,076.70.
Lump sum or instalments — how do I decide?
Compute the present value of the instalment stream at a realistic discount rate and compare it to the lump-sum offer. If the lump sum is larger than the PV of instalments, take the lump sum and invest it yourself. If the PV of instalments is larger, the instalments are the better deal at that rate. Note that this comparison ignores tax, longevity risk, behaviour (will you actually invest the lump sum?), and credit risk on the instalment payer — all of which matter in practice.
What about inflation?
The result is nominal — today's currency units measured against future nominal cash flows. To compute a real present value (in today's purchasing power), subtract your expected inflation rate from the discount rate you enter. A 7% nominal discount rate with 2% expected inflation behaves like about a 5% real rate. Equivalently, you can leave the rate alone and treat all the cash-flow inputs as already inflation-adjusted; just be consistent across all the inputs.