Present Value Calculator: Lump Sums and Annuities

About the Present Value Calculator

The Present Value Calculator works out what money in the future is worth today. Enter the future value, the annual interest rate, how often it compounds and the number of periods, and it shows the present value: the amount you would have to invest now to end up with that future sum. Add a regular payment to find the value today of a stream of payments, such as a pension, a lease or the withdrawals you plan to take from your savings.

Payments can be deposits or withdrawals, made at the end or the start of each period, annually, semiannually, quarterly or monthly. The interest can compound at a different frequency from the payments. The calculator is the same tool as the future value calculator, opened with the present value selected, so you can also solve for the future value, the payment, the rate or the number of periods.

The calculator assumes the same interest rate, often called the discount rate, for every period and ignores fees and taxes, so the results are estimates.

How to use it

The formulas

With a rate per period $i$ and $n$ periods, the present value of a single future sum is

$$PV = \frac{FV}{(1 + i)^n}$$

The present value of $n$ equal withdrawals of $PMT$, leaving nothing at the end, is

$$PV = PMT \cdot \frac{1 - (1 + i)^{-n}}{i} \cdot (1 + i \cdot t)$$

where $t$ is 1 for payments at the start of each period and 0 at the end. When the rate compounds $c$ times a year and payments are made $p$ times a year, the rate per period is $i = (1 + r/c)^{c/p} - 1$.

Worked examples

• A future sum. 10,000 in 10 years at 5% a year is worth $10{,}000 \div 1.05^{10} = 6{,}139.13$ today.
• An annuity paid at the end of each year. 1,000 a year for 10 years at 5% is worth 7,721.73 today.
• The same annuity paid at the start of each year. Each payment arrives a year sooner, so it is worth $7{,}721.73 \times 1.05 = 8{,}107.82$.
• A starting amount alongside deposits. To reach 50,000 in 10 years at 6% compounded monthly while saving 200 a month, start with 9,466.95.

Related calculators

To see how a sum grows forward instead, use the Future Value Calculator. To compare a lump sum with the payments of a loan, the Loan Calculator works out the monthly payment and the amortization schedule, and the Compound Interest Calculator shows the growth year by year.

Privacy

Nothing is uploaded; every calculation runs in your browser and never leaves your device. The numbers you type stay on this page and are gone when you close or reload it.

Frequently asked questions