Future Value Calculator (TVM)
Project the future value of a lump sum plus recurring contributions using the time value of money formula with six compounding frequencies and annuity-due or ordinary-annuity timing.
FINANCEFuture value (FV) tells you what a sum of money today will be worth at a future date once interest compounds on the principal and on any periodic contributions. It is the foundational calculation in time value of money (TVM) and underpins retirement projections, savings-goal math, and bond pricing.
The calculator combines two pieces: the lump-sum future value FV = PV × (1 + r/n)^(nt) and, if you contribute periodically, the annuity future value FV = PMT × (((1 + r/n)^(nt) − 1) / (r/n)), with an extra (1 + r/n) multiplier when contributions arrive at the beginning of each period (annuity-due) rather than the end (ordinary annuity). Continuous compounding collapses the lump term to FV = PV × e^(rt). Worked example: $10,000 present value plus $500/month deposited at the end of each month, earning 7% APR compounded monthly for 20 years. Periodic rate r/n = 0.07/12 = 0.005833, periods nt = 240. Lump portion = 10,000 × (1.005833)^240 ≈ $40,387. Annuity portion = 500 × ((1.005833^240 − 1) / 0.005833) ≈ $260,463. Future value ≈ $300,850 with total contributions of $130,000 and total interest of about $170,850 - more than half the ending balance comes from compounding rather than your deposits, which is why starting early matters so much.
Future Value Calculator (TVM)
Compute the future value of a present sum plus optional periodic contributions using the time value of money formula. Supports annual, semiannual, quarterly, monthly, daily, and continuous compounding.
Year-by-Year Accumulation
| Year | Start Balance | Contributions | Interest | End Balance |
|---|---|---|---|---|
| 1 | $10,000 | $6,000 | $919 | $16,919 |
| 2 | $16,919 | $6,000 | $1,419 | $24,339 |
| 3 | $24,339 | $6,000 | $1,956 | $32,294 |
| 4 | $32,294 | $6,000 | $2,531 | $40,825 |
| 5 | $40,825 | $6,000 | $3,148 | $49,973 |
| 6 | $49,973 | $6,000 | $3,809 | $59,782 |
| 7 | $59,782 | $6,000 | $4,518 | $70,299 |
| 8 | $70,299 | $6,000 | $5,278 | $81,578 |
| 9 | $81,578 | $6,000 | $6,094 | $93,671 |
| 10 | $93,671 | $6,000 | $6,968 | $106,639 |
| 11 | $106,639 | $6,000 | $7,905 | $120,544 |
| 12 | $120,544 | $6,000 | $8,910 | $135,455 |
| 13 | $135,455 | $6,000 | $9,988 | $151,443 |
| 14 | $151,443 | $6,000 | $11,144 | $168,587 |
| 15 | $168,587 | $6,000 | $12,383 | $186,971 |
| 16 | $186,971 | $6,000 | $13,712 | $206,683 |
| 17 | $206,683 | $6,000 | $15,137 | $227,820 |
| 18 | $227,820 | $6,000 | $16,665 | $250,486 |
| 19 | $250,486 | $6,000 | $18,304 | $274,790 |
| 20 | $274,790 | $6,000 | $20,061 | $300,851 |
Understanding Time Value of Money
Time value of money says a dollar today is worth more than a dollar tomorrow because today's dollar can be invested and earn return. The future value formula FV = PV(1 + r/n)^(nt) compounds the present value PV at periodic rate r/n over nt periods. When you add recurring contributions PMT, the annuity portion FV = PMT × (((1+r/n)^(nt) − 1)/(r/n)) sums each deposit's individual growth. If contributions land at the beginning of each period (annuity-due), every deposit earns one extra period of interest, so the annuity term gets multiplied by (1 + r/n).
Compounding frequency matters but with diminishing returns. At 7% annual, a $10,000 lump sum over 20 years grows to $38,697 with annual compounding, $40,387 monthly, and $40,552 continuous - the gap from monthly to continuous is only ~40 basis points of total return. The continuous case FV = PV × e^(rt) is the mathematical ceiling; nothing compounds "faster." For typical rates 3-10%, jumping from annual to monthly compounding moves the needle a few percent, but going from daily to continuous is almost invisible.
Future value is the workhorse calculation behind retirement planning (will my 401(k) hit my target?), savings goals (how big is my down-payment fund in 5 years?), bond pricing (par value compounded by yield), and reverse-engineering net present value (discount future cash flows back to today). It's also the basis for the Rule of 72: years to double ≈ 72 / rate%, derived from solving 2 = (1+r)^t.
Returns shown are nominal and do not automatically adjust for inflation or taxes. For tax-advantaged accounts (Roth IRA, 401(k), HSA) the FV shown is roughly what you'll see at withdrawal. For taxable accounts, apply your marginal or capital gains rate to the interest portion. To get a real (inflation-adjusted) future value, subtract your inflation assumption from the rate before computing.