The time value of money, run backwards
A dollar today is worth more than a dollar in ten years, because today's dollar can be invested. Present value is the arithmetic of that idea: it discounts a future amount back to what it is worth right now at a given rate. It is the mirror image of the Future Value Calculator — and the foundation under bond prices, lease-vs-buy decisions, pension lump-sum offers and every discounted-cash-flow valuation.
For the annuity mode, i is the per-period rate (annual rate ÷ payments per year) and n the total number of payments; payments are modeled at the end of each period (an ordinary annuity).
Worked examples
Lump sum: $10,000 arriving in 10 years, discounted at 5% compounded annually, is worth $6,139.13 today — the other $3,860.87 is the interest that money would earn. Annuity: $100 a month for 10 years at 5% is worth about $9,428.14 today, against $12,000 of total payments.
How to use this calculator
- Choose the lump-sum mode for one future amount, or the annuity mode for a stream of payments (pension, lease, settlement).
- Enter the amount(s), the annual rate and the time horizon.
- For lump sums, pick how often interest compounds — more frequent compounding lowers the present value slightly.
- Compare the result against any lump-sum offer in front of you: an offer below the present value is priced in the payer's favor.
Choosing a discount rate
The rate is the whole argument. Use a safe return (Treasury yields) to value guaranteed money, an investment return for expected money, and a higher rate for risky promises — a risky $10,000 should be discounted harder than a certain one. Pension lump-sum offers are exactly this calculation with the plan's chosen rate, which is why a low-rate environment produces surprisingly large offers.