Time Value of Money Calculator
Calculate present value, future value, and annuity growth.
Future Value
Fill in the known value, rate, and periods to see the result.
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The Core Concept
Time value of money is the foundational idea behind almost every finance calculation: a dollar today is worth more than a dollar in the future, because a dollar today can be invested and start earning a return immediately. That gap between "now" and "later" is exactly what an interest rate quantifies, and present value / future value calculations are simply the tools for moving a cash flow forward or backward across that gap.
The Formulas
FV = PV × (1 + r)^n
PV = FV ÷ (1 + r)^n
With periodic payments: FV = PV(1+r)^n + PMT × [((1+r)^n − 1) ÷ r]
r is the interest rate per period (as a decimal) and n is the number of periods. The annuity term — the part involving PMT — adds the future value of a series of equal, regularly-spaced payments on top of whatever a single starting lump sum would grow to on its own.
Worked Example: PV → FV (Lump Sum)
You invest $1,000 today at a 5% annual return for 10 years, with no additional contributions.
Worked Example: FV → PV (Reverse)
You want $10,000 in 5 years, and expect a 4% annual return. How much do you need to invest today?
Investing $8,219.27 today at 4% annually grows to exactly $10,000 in 5 years — the two calculations are mirror images of the same relationship.
Worked Example: An Annuity (Recurring Savings)
You save $200 per month at a 6% annual return (0.5% per month) for 5 years (60 months), starting from $0.
Notice the total contributed over 5 years is only $12,000 (200 × 60) — the remaining $1,954.01 is entirely from compounding growth on the earlier contributions, which is the core value proposition of investing consistently over time rather than saving the same total amount in cash.
Frequently Asked Questions
What does "time value of money" actually mean?
A dollar available today is worth more than a dollar received at some point in the future, because today's dollar can be invested and earn a return in the meantime. This single idea underlies nearly all of corporate finance and investment analysis — comparing cash flows at different points in time requires converting them to a common point using an interest rate, which is exactly what present value and future value calculations do.
What's the difference between present value and future value?
Future value answers "what will this amount grow to by a future date, given a rate of return?" Present value answers the reverse: "what is a future amount worth today, given the same rate?" They're the same relationship solved for different variables.
Why does the interest rate need to match the period length?
The rate and the period count have to describe the same unit of time — if periods are months, the rate must be a monthly rate; if periods are years, the rate must be annual. Mixing a monthly period count with an annual rate (or vice versa) without converting produces a badly wrong answer, since the formula assumes one consistent compounding period throughout.
What is the annuity formula for, specifically?
It handles a series of equal, regularly-spaced payments — a recurring deposit, a loan payment, a subscription — rather than a single lump sum. The payment amount is added on top of ordinary lump-sum growth, so this calculator can handle a starting balance, a recurring payment, or both together.
What if I don't have any recurring payments, just a single amount?
Leave the payment field blank or at 0 — the calculator falls back to the simple lump-sum formula (FV = PV × (1+r)^n) automatically, since a zero payment contributes nothing to the annuity term.
Does this calculator handle NPV directly?
Not as a separate named output, but the underlying present value math is the same building block NPV is built from — NPV sums the present values of multiple future cash flows and subtracts an initial investment. For a single cash flow's present value, this calculator gives you exactly that piece of the NPV calculation.
Why does a small change in the interest rate make such a big difference over many periods?
Because growth compounds — each period's return applies not just to your original amount but to all previously accumulated growth too. Over a small number of periods the difference between, say, 5% and 6% is minor, but over 20-30 periods it compounds into a substantial gap, which is why interest rate assumptions matter so much in long-horizon finance problems.
Is this the same math my financial calculator (like a BA II Plus) uses?
Yes — the core TVM formulas here are the same standard equations built into financial calculators used in finance coursework. The main difference is presentation: a dedicated financial calculator lets you toggle any of the five TVM variables (N, I/Y, PV, PMT, FV) as the unknown, while this tool is organized around solving specifically for PV or FV.