Present Value Calculator

A present value calculator shows what a sum of money received in the future is worth today. By entering a future amount, discount rate and number of years until receipt, the tool calculates the present value of that amount. This version offers additional features.

For example, you can calculate the value of a series of regular payments like an annuity, examine how sensitive the result is to changes in interest rates or work backwards to find out what interest rate or length of time would be required.

What is present value?

Present value is the current worth of a sum that you will receive or pay out in the future. It's based on the time value of money. Money available today is more valuable than money to be received in the future because it can be invested and earn a return. This difference comes from two factors: First, opportunity cost, which is the lost gains by choosing to wait. Second, inflation, which reduces the purchasing power of a dollar over time. When calculating present value, these two factors are combined into one interest rate so that different cash flows at different times can be compared on an equal basis.

How to use this calculator:

First enter the three main parameters: future value, annual discount rate and number of years until receipt. Select the compounding frequency to get the present value of a lump sum received in the future. Then select any desired options. By selecting "Regular cash flows" you can calculate the value of an annuity, i.e. the value of a series of equal payments, and specify the payment frequency and whether they are made at the beginning or end of each period.

By selecting "Sensitivity range" you can see results for high and low discount rates. This is important because the discount rate is often the most uncertain factor. This calculator can also be used in reverse. If one of the four main fields is left blank and the other three are filled in, the blank field will be calculated. Whether it's the required interest rate or the waiting period.

Formula understanding

For a single future amount, we use the discounting with compound interest formula.

FV is the future value, r is the annual discount rate in decimal form, k is the number of periods per year for which interest will be compounded, and n is the number of years. For example, if someone lends you $50,000 and you pay it back over 5 years with an annual interest rate of 5 percent, then r would equal .05, k would be 1, and n would be 5.

So the $50,000 you will receive in five years is worth about $39,176 today at that interest rate. The table below shows each of these inputs with example values.

Comparison of present and future value

Present value and future value are two sides of the same coin in compound interest calculations. Future value looks at an amount in the present and asks how much it has grown over time. Present value looks at an amount in the future and asks what that would be worth today. If a future value calculator shows that $1,000 today will grow to $1,629 after ten years with 5% interest, then a present value calculator will discount the same amount of $1,629 back to $1,000. Because they are inverse calculations, this tool can be used in both directions. If you leave future value blank, it will compound the current amount. If you leave present value blank, it will discount a future amount.

Present value of a pension benefit.

It is rare that funds are received in a single lump sum. Pensions, lease payments, bond coupons and loan repayments are usually a series of equal amounts. The present value of an annuity is calculated by discounting each individual payment to its current value and then adding them together. The present value of an ordinary annuity, which pays at the end of each period, is as follows:

If the payments are to be made at the beginning of each period (an "annuity due"), then the present value is slightly higher, because each payment has a shorter discounting time. The timing options in this calculator allow for both cases. Selecting "Regular Cash Flows" will calculate both the total amount and the value of the cash flow stream simultaneously.

Other present value calculations:

Some related concepts extend the same logic. A perpetuity is an annuity with no end date and its present value can be simplified to payment divided by rate, or PMT divided by r. A growing annuity increases each individual payment by a fixed percentage, which is suitable for increasing dividends or rents. Net present value (NPV) applies discounting to the whole project, summing the present values of all expected inflows and outflows, with a positive result meaning that the project's worth exceeds its cost. All these calculations use the same core mechanism and discount future cash flows using rates which take account of time and risk.

Applications of present value:

Present value helps answer questions involving real money transactions. It shows how much you should pay today for an investment that will earn a profit in the future. For example, it can compare the lump sum of a lottery win to an annuity or evaluate bonds and their coupons. Businesses use it to price assets and lease agreements and decide whether a project exceeds the cost of capital. When deciding between receiving money now or later, present value allows you to compare both options on an equal basis.

Tips for choosing a suitable discount rate:

The discount rate is an important factor that significantly affects the results. So choose it carefully. The higher the interest rate, the higher the expected return for waiting and the lower the present value. The lower the interest rate, the higher the present value. For low-risk cash flows, rates close to bond yields are appropriate. For high-risk cash flows, a risk premium should be added. If future amounts are stated in a future currency, use an interest rate that accounts for inflation. If they're stated in today's purchasing power, use a real interest rate that has been stripped of the effects of inflation. Turn on the sensitivity analysis section to see how much the results change if only the interest rate is varied.