Present and Future Value Calculator
Find the present or future value of a lump sum and a payment series, as an ordinary annuity or annuity due, at any compounding frequency, with the formula.
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About this toolWhat is the Present and Future Value Calculator?
The Present and Future Value Calculator moves money through time. Future value (FV) answers what a sum today, plus regular payments, will be worth after a number of years at a given rate. Present value (PV) answers the reverse: what a future sum, plus a stream of payments, is worth in present-day money when discounted at your required rate.
You can value a single lump sum, a level series of payments, or both at once. Payments can be yearly, every six months, quarterly, monthly, every two weeks or weekly, made at the end of each period (an ordinary annuity) or at the start (an annuity due). Compounding can be annual through daily or continuous, independent of the payment frequency.
The result splits the total into the lump-sum part and the payment part, shows the rate per period and every factor used, and charts the value year by year.
- Solve for present value or future value
- Lump sum, level payment series or both combined
- Ordinary annuity and annuity due
- Annual to daily and continuous compounding, independent of payment frequency
- Formula panel with rate per period, number of periods and growth factor
- Year-by-year chart split into lump-sum and payment parts
How to use the Present and Future Value Calculator
- Choose whether to solve for future value or present value.
- Enter the lump sum (today's amount for FV, the future amount for PV) and the payment per period. Either can be 0.
- Enter the annual rate, how often it compounds, the term in years and how often payments are made.
- Choose whether payments happen at the end of each period (ordinary annuity) or at the start (annuity due).
- Read the total, the split between lump sum and payments, the formula with the rate per period and the year-by-year chart.
Worked examples
Future value of savings plus a monthly payment
Input
FV, 10,000 today, 200 a month, 6% compounded monthly, 10 years, end of month
Output
FV 50,969.84 (lump sum 18,193.97 + payments 32,775.87)
The rate per month is 0.5% and the growth factor over 120 months is 1.819397. Of the total, 34,000 is money paid in and 16,969.84 is interest.
Present value of a future sum
Input
PV, 50,000 in 8 years, 5% compounded annually, no payments
Output
PV 33,841.97
This is what you would need to invest today at 5% to have 50,000 in eight years, or what a promise of 50,000 in eight years is worth to someone who could earn 5% elsewhere.
Lump-sum value of a pension
Input
PV, 1,500 a month for 20 years, 4% compounded monthly, start of month
Output
PV 248,357.90 (end of month: 247,532.79)
Comparing a pension's monthly income with a lump-sum offer starts here. Payments at the start of each month are worth 825 more because each arrives a month sooner.
Annuity due vs ordinary annuity over 30 years
Input
FV, 5,000 a year, 7% annually, 30 years
Output
Start of year 505,365.21; end of year 472,303.93
Contributing at the start of each year instead of the end adds 33,061, exactly 7% more, because the annuity due result is the ordinary result times 1.07.
Background and insight
Every time value of money calculation rests on one growth factor, (1 + i)^n, where i is the interest rate per period and n is the number of periods. A lump sum grows by multiplying by it: FV = PV × (1 + i)^n. Discounting divides by it: PV = FV ÷ (1 + i)^n. A level payment series sums those factors for each payment, which collapses to the annuity formulas FV = PMT × [((1 + i)^n − 1) ÷ i] and PV = PMT × [(1 − (1 + i)^−n) ÷ i].
An annuity due pays at the start of each period, so each payment has one more period to grow or one less to be discounted. Both formulas are multiplied by (1 + i). Rent, insurance premiums and many savings plans are annuities due; loan repayments and bond coupons are ordinary annuities. With 1,000 a year for 10 years at 5%, the ordinary annuity has a PV of 7,721.73 and the annuity due 8,107.82, the same numbers found in standard annuity tables.
When compounding and payments happen at different frequencies, the calculator converts the nominal annual rate r with i = (1 + r/m)^(m/p) − 1, where m is compounding periods a year and p is payments a year, or i = e^(r/p) − 1 for continuous compounding. This is the method financial calculators use when P/Y and C/Y differ. The effective annual rate is shown too, so you can compare results with an APY.
Common use cases
Finance coursework and exams
Check textbook answers for PV, FV, ordinary annuity and annuity due problems, with the factors shown.
Lump sum or payments decisions
Compare a lottery, pension or settlement lump sum against the present value of the payment stream.
Savings targets
See what a starting balance plus regular contributions grows to at a given return.
Pricing a stream of income
Value a lease, royalty or structured settlement by discounting its payments at your required rate.
Tips and limitations
- All amounts are treated as flowing in the same direction. To net a cost against a benefit, run them separately and subtract, or use the NPV and IRR Calculator for mixed signs.
- A term that is not a whole number of payment periods (for example 2.3 years of monthly payments) is valued with a fractional number of periods. Round the term if your payments stop at a whole period.
- The discount rate drives present value more than anything else. A 30-year stream at 4% is worth much more than at 7%; try both.
- Continuous compounding is mainly used in derivatives pricing and textbooks. Savings and loans usually compound daily or monthly.
- For a payment stream that never ends, present value is payment ÷ rate (a perpetuity). Very long terms in this calculator approach that limit.
Frequently asked questions
What is the difference between present value and future value?
Future value grows money forward: what an amount today becomes after earning interest. Present value discounts money back: what an amount received later is worth today. They use the same factor, (1 + i)^n, multiplied in one direction and divided in the other.
What is the formula for the present value of an annuity?
For an ordinary annuity, PV = PMT × [(1 − (1 + i)^−n) ÷ i]. For an annuity due, multiply by (1 + i). 1,000 a year for 10 years at 5% gives 7,721.73, or 8,107.82 as an annuity due.
Why is an annuity due worth more than an ordinary annuity?
An ordinary annuity pays at the end of each period, like loan repayments. An annuity due pays at the start, like rent. An annuity due is worth (1 + i) times more in both PV and FV because each payment is one period earlier.
How does compounding frequency affect future value?
More frequent compounding means a slightly higher effective rate. 6% compounded monthly is 6.17% effective a year, and continuously compounded it is 6.18%. The calculator converts the nominal rate to the rate per payment period so compounding and payment frequency can differ.
What discount rate should I use for present value?
Use the return you could earn elsewhere at similar risk. For a guaranteed payment that might be a government bond yield, for a business cash flow the company's cost of capital. A higher rate always means a lower present value.
Does this calculator match Excel PV and FV?
Yes for the same inputs. Excel's FV(rate, nper, pmt, pv, type) and PV(rate, nper, pmt, fv, type) return negative numbers for positive inputs because of their sign convention; this calculator shows the same magnitudes as positive values. Type 1 in Excel is the annuity due option here.
Is there an in-depth guide to the Present and Future Value Calculator?
Yes. “Time Value of Money: PV, FV, NPV, IRR, CAGR and ROI Explained” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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