The future value formula
Future value is what an amount becomes after earning a compound rate for a number of periods: FV = PV × (1 + i)^n, where i is the rate per period and n the number of periods. $10,000 at 6% a year for ten years grows to 10,000 × 1.06^10 = $17,908. The factor (1 + i)^n is the growth factor, the exact inverse of the present value calculator's discount factor.
The table shows a $10,000 lump sum at four rates. Over long periods the rate dominates: at 3% the money roughly triples in forty years; at 10% it multiplies more than forty-fold.
| After | At 3% | At 5% | At 7% | At 10% |
|---|---|---|---|---|
| 1 years | $10,300.00 | $10,500.00 | $10,700.00 | $11,000.00 |
| 5 years | $11,592.74 | $12,762.82 | $14,025.52 | $16,105.10 |
| 10 years | $13,439.16 | $16,288.95 | $19,671.51 | $25,937.42 |
| 20 years | $18,061.11 | $26,532.98 | $38,696.84 | $67,275.00 |
| 30 years | $24,272.62 | $43,219.42 | $76,122.55 | $174,494.02 |
| 40 years | $32,620.38 | $70,399.89 | $149,744.58 | $452,592.56 |
Future value of a series of payments
Regular payments each grow for a different length of time — the first for n periods, the last for none — and the sum collapses to FV = PMT × [(1 + i)^n − 1] ÷ i for payments at the end of each period. This is the formula behind every savings plan and every retirement projection. The table gives $1,000 a year.
| Rate | 10 years | 20 years | 30 years |
|---|---|---|---|
| 2% | $10,949.72 | $24,297.37 | $40,568.08 |
| 4% | $12,006.11 | $29,778.08 | $56,084.94 |
| 6% | $13,180.79 | $36,785.59 | $79,058.19 |
| 8% | $14,486.56 | $45,761.96 | $113,283.21 |
| 10% | $15,937.42 | $57,275.00 | $164,494.02 |
Compounding frequency
The same annual rate compounded more often produces a slightly higher future value, because interest starts earning interest sooner. The effect is modest — the difference between annual and daily compounding at 6% over ten years is about 3% of the result — and it tails off quickly: daily and continuous compounding are nearly indistinguishable. Choose the frequency your investment actually uses.
| Compounded | Future value |
|---|---|
| Annually | $17,908.48 |
| Semi-annually | $18,061.11 |
| Quarterly | $18,140.18 |
| Monthly | $18,193.97 |
| Daily | $18,220.29 |
| Continuously | $18,221.19 |
Payments at the beginning versus the end of the period
A payment made at the start of each period earns one extra period of interest. Over a long plan the difference equals one period's growth applied to the whole payment stream, about 6% of the payment total at a 6% rate. If you contribute at the start of each month or year, choose 'Beginning'.
| Years | End of period | Beginning of period | Difference |
|---|---|---|---|
| 5 years | $5,637.09 | $5,975.32 | $338.23 |
| 10 years | $13,180.79 | $13,971.64 | $790.85 |
| 20 years | $36,785.59 | $38,992.73 | $2,207.14 |
| 30 years | $79,058.19 | $83,801.68 | $4,743.49 |
Reading the schedule
The schedule lists every compounding period: the balance at the start, the payment added, the interest earned and the closing balance. Interest each period is the balance (plus the payment, if made at the start) times the period rate. Year-end subtotals make it easy to see how much interest each year added, and the CSV export drops into a spreadsheet for further modelling.
- FV of a lump sum = PV × (1 + i)^n.
- FV of payments at the end of each period = PMT × [(1 + i)^n − 1] ÷ i.
- FV of payments at the beginning of each period = the above × (1 + i).
- Period rate i = annual rate ÷ compounding periods per year; n = years × periods per year.
Future value in planning
Use future value to see what today's savings become, to inflate a cost to a future date (a $30,000 tuition bill at 5% education inflation is about $49,000 in ten years), or to check a projection someone else has given you. It assumes a constant rate; real investment returns vary, so treat the result as a central estimate and run a lower rate to see the downside. The investment calculator adds an inflation adjustment and solves for the payment or rate a target needs; the present value calculator runs the same math backwards.