The Present Value Calculator finds the value today of a future sum of money, or of a series of equal periodic deposits, given an interest (discount) rate and number of periods.
Find the present value of a single lump sum to be received in the future.
Find the present value of a stream of equal deposits made each period.
The present value calculator determines how much a future amount of money is worth in today's dollars. It answers one of the most fundamental questions in finance: if you are promised a sum of money at some point in the future, what is that promise worth right now? Because money available today can be invested to earn a return, a dollar received in the future is worth less than a dollar received today. Present value (PV) quantifies exactly how much less, given an interest rate and a time horizon. This tool calculates the present value of a single future lump sum as well as the present value of a series of equal periodic deposits (an annuity).
Present value is the foundation of nearly all financial valuation - it underlies bond pricing, loan analysis, investment appraisal, retirement planning, and the discounted cash flow models used to value companies and projects.
Present value is the current worth of a future sum of money or stream of cash flows, given a specified rate of return. The concept rests on the time value of money - the principle that a given amount of money is worth more the sooner it is received, because it can be put to work earning interest. Present value reverses the compounding process: instead of growing a present amount forward into the future, it discounts a future amount backward to the present.
The interest rate used in this process is often called the discount rate, because it discounts future dollars to their present worth. A higher discount rate means future money is worth less today; a lower discount rate means it is worth more.
For a single future lump sum, present value is calculated as:
PV = FV ÷ (1 + r)n
Where PV is the present value, FV is the future value, r is the interest (discount) rate per period, and n is the number of periods. Example: The present value of $1,000 to be received in 10 years, discounted at 6% per year, is $1,000 ÷ (1.06)10 = $1,000 ÷ 1.790847 = $558.39. The difference between the future value and the present value - $441.61 - represents the total interest, or the cost of waiting ten years for the money.
When money arrives as a series of equal payments each period rather than a single lump sum, you calculate the present value of an annuity. For deposits made at the end of each period (an ordinary annuity), the formula is:
PV = PMT × [1 − (1 + r)−n] ÷ r
Where PMT is the payment each period. Example: The present value of $100 deposited at the end of each year for 10 years, at 6%, is $100 × [1 − 1.06−10] ÷ 0.06 = $736.01. Over those ten years you deposit $1,000 in total (the principal), which grows to a future value of $1,318.08, of which $318.08 is interest.
If deposits are made at the beginning of each period (an annuity due), each payment has one extra period to earn interest, so both the present and future values are higher - the ordinary-annuity result is simply multiplied by (1 + r).
Present value is one of the most important concepts in all of finance because it lets you compare money across different points in time on an equal footing. Without it, you cannot meaningfully compare, say, $10,000 today against $12,000 in five years. By discounting the future amount to its present value, you can determine which is actually worth more given your required rate of return. This single idea powers an enormous range of real-world decisions:
Present value and future value are two sides of the same coin. Future value answers "what will an amount today grow to?" by compounding it forward, while present value answers "what is a future amount worth today?" by discounting it backward. They use the same variables and are mathematically inverse: PV = FV ÷ (1 + r)n, and FV = PV × (1 + r)n. Whether you compound or discount simply depends on which direction in time you are moving.
The discount rate is the single most influential input in any present value calculation, and choosing it appropriately is crucial. It represents the rate of return you could earn on an alternative investment of similar risk - your opportunity cost of capital. Key points about the discount rate:
The amount of money you expect to receive (or pay) at a future date. For the annuity calculator, this is replaced by the periodic deposit amount.
How many periods separate the present from the future amount. The longer the time horizon, the more a future amount is discounted and the smaller its present value.
The discount rate per period, expressed as a percentage. Make sure the rate and the number of periods use the same time unit - both annual, or both monthly, and so on.
For the annuity calculator, the equal amount deposited each period. The timing setting controls whether deposits occur at the beginning or end of each period.
Suppose you win a prize and can choose either $50,000 today or $6,000 per year for 10 years. Which is better? At first glance the annuity totals $60,000, more than the lump sum. But to compare them fairly you must find the present value of the annuity. At a 6% discount rate, the present value of $6,000 per year for 10 years is about $44,160 - less than the $50,000 lump sum. So despite the larger nominal total, the lump sum is worth more today. Change the discount rate and the answer can flip, which is exactly why present value analysis is essential to such decisions.
Present value is a powerful tool, but it has limitations to keep in mind:
Present value is what a future amount of money is worth today. Because money can earn interest over time, a sum received in the future is worth less than the same sum received now. Present value tells you exactly how much less.
Future value grows a present amount forward in time using compound interest; present value discounts a future amount backward to today. They are mathematical inverses of each other and use the same inputs.
Use a rate that reflects your opportunity cost - the return you could earn on a comparable alternative investment - adjusted for the risk of the future cash flows. Common choices include a market interest rate, an expected investment return, or a company's cost of capital.
A higher rate means your money could grow faster if you had it today, so a fixed future amount represents a smaller present investment. Discounting at a higher rate therefore produces a lower present value.
It is the value today of a series of equal future payments. It equals the sum of the present values of each individual payment, and this calculator computes it directly for both ordinary annuities (end-of-period) and annuities due (beginning-of-period).
Investors compare the present value of an investment's expected future cash flows to its current price. If the present value exceeds the price, the investment may be worthwhile. This is the core of net present value (NPV) analysis and discounted cash flow valuation.