How to use this calculator
- Calculate. Choose Future value to grow money forward, or Present value to find what future money is worth today.
- Starting amount (future value mode) or lump sum in the future (present value mode). Use $0 if you only have payments.
- Payment each period and how often payments are made. Interest compounds on the same schedule. Use $0 for a lump sum only.
- Annual interest rate and years.
- Payments at the end or start of each period: end is an ordinary annuity, start is an annuity due.
- Under Growing annuity, add a yearly growth rate if each payment should be larger than the one before.
The results break the answer into its parts, show each formula with your numbers in it, and give a year-by-year table you can download.
The formulas
The calculator uses the rate per period, i = annual rate ÷ periods per year, and the number of periods, n = years × periods per year. For monthly payments at 6% over 10 years, i = 0.005 and n = 120.
A lump sum grows and discounts like this:
A level payment stream (ordinary annuity, payments at the end of each period):
For an annuity due (payments at the start of each period), multiply either result by (1 + i).
A growing payment stream, where the first payment is PMT and each one after is (1 + g) times the last:
Here g is the yearly growth rate divided by the periods per year. When g equals i the formulas divide by zero, so the calculator uses their limits instead: FV = n × PMT × (1 + i)^(n − 1) and PV = n × PMT ÷ (1 + i).
Worked example: future value
You have $10,000 and add $200 a month at 6% for 10 years, with deposits at the end of each month.
- i = 0.06 ÷ 12 = 0.005 and n = 10 × 12 = 120
- Starting amount: 10,000 × 1.005^120 = 10,000 × 1.819397 = $18,193.97
- Payments: 200 × (1.005^120 − 1) ÷ 0.005 = 200 × 163.8793 = $32,775.87
- Future value: 18,193.97 + 32,775.87 = $50,969.84
You put in $34,000; interest adds about $16,970. Making the same deposits at the start of each month raises the total to $51,133.72. Making start-of-month deposits that grow 3% a year (a growing annuity due) brings it to $55,985.44.
Worked example: present value
How much would you need today to have $50,000 in 10 years at 6%? Compounded monthly, PV = 50,000 ÷ 1.005^120 = $27,481.64. Compounded once a year it’s 50,000 ÷ 1.06^10 = $27,919.74.
Present value works for income streams too. A pension paying $2,000 a month for 25 years, discounted at 5%, is worth $342,120.09 today. If the payment rises 2.5% a year, its present value is $445,147.68. That gap is why a cost-of-living adjustment is worth so much.
Ordinary annuity vs annuity due
With $1,000 a year for 5 years at 10%, moving each payment to the start of the year adds one year of interest to every payment:
| Ordinary annuity (end) | Annuity due (start) | |
|---|---|---|
| Future value | $6,105.10 | $6,715.61 |
| Present value | $3,790.79 | $4,169.87 |
Both annuity-due figures are exactly 1.1 times the ordinary-annuity ones. Savings deposits and loan payments usually fall at the end of the period; rent, leases and insurance premiums are usually paid in advance.
How rate and time change a lump sum
What $10,000 grows to, and what $100,000 in the future is worth today, at monthly compounding:
| Rate | FV in 10 years | FV in 20 years | FV in 30 years | PV of $100,000 in 10 years | in 20 years | in 30 years |
|---|---|---|---|---|---|---|
| 3% | $13,494 | $18,208 | $24,568 | $74,110 | $54,922 | $40,703 |
| 5% | $16,470 | $27,126 | $44,677 | $60,716 | $36,864 | $22,383 |
| 7% | $20,097 | $40,387 | $81,165 | $49,760 | $24,760 | $12,321 |
| 9% | $24,514 | $60,092 | $147,306 | $40,794 | $16,641 | $6,789 |
Future value and present value are mirror images: each present value is $100,000 divided by the same growth factor that turns $10,000 into the future value on its left.
Tips for using the results
- Match the rate to the risk. A guaranteed amount should be discounted at a safe rate; an uncertain one deserves a higher rate.
- Think in real terms for long horizons. Subtract expected inflation from the rate to see results in today’s dollars, or check the effect with the inflation calculator.
- For detailed savings plans, the investment calculator and retirement calculator add contributions over time, and the annuity calculator models payouts from a lump sum.
- For interest that doesn’t compound, use the simple interest calculator.
Assumptions & limitations
The rate is constant, payments and compounding happen on the same schedule, and the annual rate is divided evenly across periods (a nominal rate). The number of periods is rounded to a whole number. Growth applies every period, so monthly payments rise slightly each month rather than once a year. Results are before taxes, fees and inflation. Real investment returns vary from year to year.
Sources
This calculator is for education. It’s not investment advice, and actual returns are never guaranteed.
Frequently asked questions
What is the future value formula?
For a single amount, FV = PV × (1 + i)^n, where i is the rate per period and n is the number of periods. For a level payment at the end of each period, FV = PMT × [(1 + i)^n − 1] ÷ i. The calculator adds the two together when you have a starting amount and regular payments.
What is present value?
Present value is what a future amount is worth today, given a rate of return you could earn in the meantime. $50,000 received in 10 years is worth $27,481.64 today at 6% compounded monthly, because that much invested now at 6% would grow to $50,000. The higher the rate or the longer the wait, the lower the present value.
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity, payments come at the end of each period, like most loan payments and savings deposits. In an annuity due, they come at the start, like rent or insurance premiums. Each payment in an annuity due has one more period to earn interest, so both its future and present value are higher by a factor of (1 + i).
What is a growing annuity?
A growing annuity is a series of payments that rises by a fixed percentage each period, such as savings that increase with your pay. The formula replaces the level-payment factor with [(1 + i)^n − (1 + g)^n] ÷ (i − g) for future value. Set a payment growth rate under Growing annuity to use it.
What rate should I use to discount future money?
Use the return you could reasonably earn on money of similar risk over the same period. For a guaranteed payment, a Treasury or CD rate is a sensible benchmark; for a goal funded with stock investments, many people use a long-run expected return. A higher discount rate always gives a lower present value.
Why does compounding frequency change the answer?
The calculator divides the annual rate by the number of periods per year, so more frequent periods mean slightly faster growth. 6% compounded monthly has an effective annual rate of 6.168%. The results show that effective rate so you can compare options on equal terms.
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.