Time Value of Money (TVM) Calculator

Pick the variable to solve for — future value, present value, monthly payment, or number of years — then enter the other three plus an annual rate. You'll get the answer with all five TVM variables laid out.

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How the time value of money works

The time value of money is the single idea underneath almost all of finance: a dollar today is worth more than a dollar later, because today's dollar can earn interest in the meantime. Loans, mortgages, retirement plans, bond prices, and lottery "lump sum vs. annuity" choices are all the same five-variable equation wearing different costumes: present value, payment, rate, time, and future value. Fix any four and the fifth is determined — this calculator solves for whichever one you pick.

It answers the four questions people actually ask: What will my money grow to? (future value), What is a future amount worth today? (present value), How much do I need to save each month? (payment), and How long will it take? (years).

The formula

FV = PV × (1 + i)n  +  PMT × ((1 + i)n − 1) ÷ i

PV is the present value, PMT the payment made at the end of each month, FV the future value, n the number of months, and i the monthly rate (annual rate ÷ 12 ÷ 100). This calculator compounds monthly and rearranges the same equation to solve for whichever variable you choose; solving for n uses logarithms, and a zero rate falls back to simple addition.

Worked example

Solve for future value: $10,000 today plus $200 at the end of each month, at 5% compounded monthly for 10 years. With i = 0.05 ÷ 12 and n = 120, the lump sum grows to about $16,470 and the payments to about $31,056 — a future value of $47,526.55.

Solve for years: $5,000 today, $300 per month at 6%, aiming for $100,000: n = ln((FV·i + PMT) ÷ (PV·i + PMT)) ÷ ln(1 + i) ≈ 181 months, so about 15.1 years.

A word on sign conventions

Financial calculators and spreadsheets use a cash-flow convention where money leaving your pocket is negative, which is why Excel's FV function returns negative numbers and confuses everyone. This calculator keeps it simple: contributions are positive, and everything is from the saver's point of view. If you enter a negative monthly payment, it's treated as a withdrawal — useful for "how long will my nest egg last"-style questions. And if the withdrawals outrun the interest, the goal is mathematically unreachable at any horizon; the calculator will tell you instead of pretending otherwise.

Frequently asked questions

What is the time value of money?

It's the principle that a dollar today is worth more than a dollar in the future, because today's dollar can earn interest in the meantime. Every loan, mortgage, and retirement plan is priced off this idea — it's the foundation the rest of finance is built on.

What formula does a TVM calculator use?

FV = PV × (1 + i)^n + PMT × ((1 + i)^n − 1) ÷ i, where i is the monthly rate (annual rate ÷ 12 ÷ 100), n is the number of months, and payments land at the end of each month. Solving for PV or PMT rearranges the equation; solving for n uses logarithms.

How long will it take to reach my savings goal?

Choose "Number of years" mode and enter what you have, what you'll add monthly, your rate, and the target. For example, $5,000 today plus $300 a month at 6% reaches $100,000 in about 15 years.

Why does the calculator say my goal is unreachable?

If your monthly payment is negative (a withdrawal) and larger than the interest the balance earns, the account shrinks every month instead of growing — so no number of years will ever reach the target. Reduce the withdrawal or raise the rate and it becomes solvable.

Why does Excel's FV function give a negative number when this doesn't?

Spreadsheets use a cash-flow sign convention where money leaving your pocket is negative, so deposits are entered as negatives and results flip sign. This calculator uses the simpler saver's view: contributions are positive, and a negative payment explicitly means a monthly withdrawal.

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