Calculate the future value of a present amount at a fixed interest rate.
FV = PV × (1 + rate)ⁿ = 8,000 × (1 + 5%)^8 = 11,819.64.
This calculator solves the fundamental time-value-of-money equation used across virtually all financial planning: loans, savings, annuities, and investments. It relates present value, future value, payment, interest rate, and number of periods — give it any four and it solves for the fifth.
PV is present value, FV is future value, PMT is the periodic payment, r is the periodic interest rate, and n is the number of periods. This single relationship underlies mortgage calculations, retirement projections, savings goals, and loan amortization.
| Goal | Known variables | Solving for |
|---|---|---|
| Loan payment | PV, rate, term | PMT |
| Savings goal | FV target, rate, term | PMT |
| Investment growth | PV, PMT, rate, term | FV |
| Required return | PV, FV, term | rate |
Example 1 — Future value of a lump sum: $8,000 invested today at 5% annual interest for 8 years, no additional contributions: FV = 8,000 × (1.05)⁸ ≈ $11,820.
Example 2 — Solving for required rate: To grow $10,000 into $20,000 over 10 years with no added contributions requires an annual rate of about 7.2% — found by solving (1+r)¹⁰ = 2.
Example 3 — Savings goal with monthly payments: To reach $50,000 in 10 years at a 6% annual return (0.5%/month), with an existing $5,000 starting balance, requires monthly contributions of roughly $260, combining both the growth of the initial balance and the compounding contributions.
| Term | Meaning |
|---|---|
| PV (Present Value) | Value of money today |
| FV (Future Value) | Value of money at a future date |
| PMT (Payment) | Recurring cash flow each period |
| Discount rate | Rate used to bring future money back to present value |
| Annuity | A series of equal, regular payments |
Why does the order of variables matter? It doesn't change the math, but knowing which variable is unknown determines which rearranged form of the formula to apply.
Can this handle irregular cash flows? This formula assumes equal, regular payments; irregular cash flows require net-present-value or internal-rate-of-return methods instead.
How does this relate to a loan calculator? A loan calculation is simply this same formula with FV set to zero, since the loan balance is fully repaid by the end.
What's the difference between an ordinary annuity and an annuity due? An ordinary annuity assumes payments occur at the end of each period, while an annuity due assumes payments at the start — the annuity-due version produces a slightly higher future value since each payment compounds for one extra period.
Why is $1,000 today worth more than $1,000 in five years? Because money available today can be invested and earn a return, so its future value exceeds a fixed sum received later — this is the core idea behind the time value of money.
How is this formula used in retirement planning? The same relationship projects how a starting balance plus regular contributions grows to a target future value, which is exactly how retirement calculators estimate whether current savings are on track.
What does a negative present or future value mean in financial calculators? Many financial calculators (like Excel's PV/FV functions) use sign conventions where outgoing cash (like a payment) is negative and incoming cash (like a payout) is positive — it's a convention, not a different formula.
A present value of $10,000 growing at 5% annually for 15 periods reaches roughly $20,789 — illustrating the time-value-of-money principle that a fixed rate compounded over enough periods can roughly double an initial sum.
Present value: The current worth of a future sum of money, or vice versa.
Time value of money: The principle that money available now is worth more than the same amount in the future, due to its earning potential.