Smarter Than Free calculator
Present Value Calculator
Discount a future lump sum back to today. Optional ordinary annuity (fixed payments). Rate and periods are yours to set.
Calculator
How do you calculate present value?
PV = future value ÷ (1 + rate)^years. Higher discount rates mean a lower present value.
What rate should I use for present value?
Your opportunity cost or required return. This tool does not fetch a market rate.
What is the difference between present value and net present value?
Present value converts a future amount into today’s money. Net present value adds up the present values of every cash flow and subtracts the upfront cost. Above zero, the project beats your discount rate.
Should the discount rate include inflation?
Match the two. Discount cash flows in future pounds with a rate that includes inflation, and cash flows in today’s pounds with a real rate. Mixing them is a neat way to get a confident wrong answer.
Why do small rate changes matter so much over long periods?
Because the rate compounds across every year. £10,000 in 30 years is worth £3,083 today at 4% and £1,741 at 6%. Two percentage points, about a 44% smaller answer.
What £10,000 in the future is worth today
PV = 10,000 ÷ (1 + rate)^years. Pick the rate that matches your own alternative.
| In | At 2% | At 4% | At 6% | At 8% |
|---|---|---|---|---|
| 1y | £9,804 | £9,615 | £9,434 | £9,259 |
| 5y | £9,057 | £8,219 | £7,473 | £6,806 |
| 10y | £8,203 | £6,756 | £5,584 | £4,632 |
| 20y | £6,730 | £4,564 | £3,118 | £2,145 |
| 30y | £5,521 | £3,083 | £1,741 | £994 |
The formula
Lump sum: PV = future value ÷ (1 + rate)^periods Ordinary annuity (payment at end of each period): PV = payment × [1 − (1 + rate)^(−periods)] ÷ rate rate is the discount rate per period (5% a year with yearly periods → 0.05). If rate = 0, annuity PV = payment × periods.
Worked example
You will receive £10,000 in 5 years. Discount rate 4% a year.
PV = 10000 ÷ (1.04)^5 ≈ £8,219.27.
Ordinary annuity: £1,000 at the end of each year for 5 years at 4%.
PV = 1000 × [1 − (1.04)^(−5)] ÷ 0.04 ≈ £4,451.82.
A pound today beats a pound tomorrow when rates are positive. That is the whole joke.
Methodology
How it calculates
- Discounts a single future cash amount back to today at the rate you enter.
Formula
Lump sum: PV = future value ÷ (1 + rate)^periods Ordinary annuity (payment at end of each period): PV = payment × [1 − (1 + rate)^(−periods)] ÷ rate rate is the discount rate per period (5% a year with yearly periods → 0.05). If rate = 0, annuity PV = payment × periods.
Assumptions
- Single cashflow. No coupon schedule unless you model it yourself elsewhere.
Edge cases
- Higher discount rates produce a lower present value.
Sources
None. Pure maths; no external rate or spec feed.
FAQ
What discount rate should I use?
Something that matches the risk and the period. A savings rate, a loan rate, or a required return. This tool will not choose it for you.
Ordinary annuity vs annuity due?
Ordinary = pay at period end (most bonds and loans). Annuity due = pay at period start (some leases and rent). This calculator uses ordinary.
Can I mix a lump sum and an annuity?
Yes. Work each PV, then add them. The results panel shows them separately so you can see the pieces.
Not financial advice. This calculator is for education only. Double-check results before you make money decisions. Past moves do not predict future ones.