Time Value of Money Calculator

A time value of money (TVM) calculator solves the equation that links five variables - the number of periods (N), the interest rate, present value (PV), payment (PMT), and future value (FV) - by finding any one of them from the other four. For example, $10,000 today plus $200 a month at 6% compounded monthly grows to $50,970 in 10 years. That one engine can price a loan, project savings, value an annuity, or back out a rate of return.

Planning for retirement specifically? This page is the raw TVM math for any single scenario, but for tax-advantaged accounts reach for the dedicated tools: the Retirement Calculator for an overall nest-egg projection, the 401(k) Calculator and IRA Calculator for employer and traditional-account contribution limits, and the Roth IRA Calculator for tax-free growth. Use this calculator when you need the underlying compounding math behind any of them.

The core idea: a dollar today beats a dollar tomorrow

The time value of money is the principle that money available now is worth more than the same amount in the future, because today's money can be invested and earn a return. Put $10,000 in an account earning 6% and in a year you have $10,600; that extra $600 is the cost of waiting. Working backward, a promise of $10,600 in one year is worth only $10,000 today at a 6% discount rate. Compounding moves money forward in time (PV to FV), and discounting moves it backward (FV to PV). Every TVM calculation is one of those two motions applied to a lump sum, a stream of equal payments, or both at once.

The time value of money formula

All five variables are tied together by a single equation. Using the cash-flow sign convention, the balance of every TVM problem is:

Here r is the periodic interest rate (the annual rate divided by the number of periods per year), N is the total number of periods, and t is the payment-timing flag (0 for end-of-period payments, 1 for beginning-of-period). When there is no recurring payment, PMT is zero and the equation collapses to the familiar single-sum relationship:

Solving for FV, PV, or PMT is just algebra - rearrange the equation. Solving for N requires a logarithm. Solving for the rate has no closed-form solution, so the calculator searches for it numerically until the equation balances, which is exactly what the solver inside a physical financial calculator does.

A worked example: growing a deposit with monthly contributions

Suppose you deposit $10,000 today and add $200 at the end of every month for 10 years (N = 120 periods) in an account earning 6% annually, compounded monthly. The periodic rate is r = 6% ÷ 12 = 0.5% = 0.005. Plugging into the formula with PMT and PV as outflows, the future value works out to about $50,970. Of that, $10,000 was your initial deposit, $24,000 was the sum of your 120 monthly contributions, and the remaining ~$16,970 is compound interest the money earned along the way. Switch the calculator to "solve for PMT," enter a target FV of $75,000, and it tells you the monthly contribution needed to hit that goal instead. Switch to "solve for rate," and it finds the return that turns your deposits into a chosen future value.

How much will $10,000 plus $200 a month grow to?

This is the most common "solve for FV" question people bring to a TVM calculator. The table below computes the future value of a $10,000 starting deposit plus $200 at the end of every month, compounded monthly, across three annual rates and four horizons. Read down a column to see how time compounds, and across a row to see how the rate matters.

Future value of a $10,000 lump sum plus $200/month (ordinary annuity), monthly compounding, computed with the standard TVM equation. Rates are illustrative, not a forecast.

Time value of money table: year-by-year growth

Here is the same 10-year, 6% example broken down annually so you can watch contributions and compound interest pull apart. Early on almost all of the balance is money you put in; by year 10, interest is a large share of the total.

The cash-flow sign convention (read this first)

The most common source of confusion in TVM math is signs. Every amount is either a cash outflow (money leaving you, entered as negative) or a cash inflow (money coming to you, entered as positive). If you invest a lump sum and make ongoing deposits, both PV and PMT are negative, and the resulting FV is positive because it is money you eventually receive. For a loan it flips: the loan principal you receive is a positive PV, and the payments you make are negative. If a result comes back negative, that is not an error - it means the answer is a payment out of your pocket. Getting the signs right is what lets a single equation describe both saving and borrowing.

How to use this time value of money calculator

1. Pick what to solve for: choose N, rate, PV, PMT, or FV. That field disappears from the inputs because the calculator will compute it.
2. Enter the number of periods (N): if you compound monthly for 10 years, that is 120 periods - not 10. Always match N to your compounding frequency.
3. Enter the annual interest rate: type the yearly nominal rate as a percent; the tool converts it to a periodic rate automatically.
4. Set the compounding frequency: annual, semiannual, quarterly, monthly, weekly, or daily. This sets both the periodic rate and the meaning of N.
5. Enter present value, payment, and future value: fill the three you know, using negative numbers for money you pay out and positive for money you receive. Leave zero where a piece does not apply.
6. Choose payment timing: end of period (ordinary annuity) or beginning of period (annuity due).

Press Calculate and the missing variable appears, along with the periodic rate, compounding frequency, and whether the result is an inflow or outflow.

Ordinary annuity vs. annuity due

Whether payments land at the end or the beginning of each period matters. An ordinary annuity (end of period) is the default for most loans and bonds - the first payment is one period away. An annuity due (beginning of period) is typical of rent and many leases, where you pay up front. Because annuity-due payments sit in the account one extra period, they earn slightly more interest, so both present and future values are larger by a factor of (1 + r). The toggle in the calculator lets you compare the two; for a long horizon the difference can be meaningful.

Who this calculator is for

• Finance and accounting students learning TVM who want to check homework or replicate an HP 12C / TI BA II Plus without buying one.
• Savers projecting how a lump sum plus regular contributions grows toward a goal.
• Borrowers backing out a loan payment from a principal, rate, and term, or finding the rate baked into a financing offer.
• Investors computing the present value of a future payout, or the implied annual return that turns deposits into a target.
• Anyone comparing offers - a lump sum now versus a stream of payments later - on an apples-to-apples basis.

A second worked example: present value of a future sum

Imagine you are promised $50,000 in 8 years and want to know what it is worth today if money can earn 5% per year, compounded annually (so N = 8, PMT = 0). Solving for PV, the answer is about $33,842. In other words, $33,842 invested today at 5% grows to $50,000 in eight years, so the future promise is worth exactly that much now. This is the heart of valuation: discounting future cash flows back to the present. Change the rate to 8% and the present value drops to roughly $27,013 - higher discount rates make future money worth less today, which is why interest-rate moves ripple through the price of bonds, annuities, and businesses.

What is $10,000 worth in the future - and what is future money worth today?

The two halves of this quick-reference table show both directions of the same math for a single $10,000 lump sum (PMT = 0). The left columns compound $10,000 forward at 5% and 7%; the right columns discount a $10,000 amount received N years from now back to today's dollars.

Single-sum future value FV = PV × (1 + r)^N and present value PV = FV ÷ (1 + r)^N, annual compounding. Rates are illustrative.

Key terms explained

• Present value (PV): what a future amount or stream of payments is worth in today's dollars.
• Future value (FV): what an amount invested or paid today will be worth at a later date.
• Payment (PMT): the equal cash flow that recurs each period - a deposit, a loan payment, or an annuity income.
• Periodic rate (r): the interest rate for one period, equal to the annual rate divided by periods per year.
• Number of periods (N): the total count of compounding/payment periods, measured in the same units as the rate.
• Discounting vs. compounding: discounting moves money backward in time (FV to PV); compounding moves it forward (PV to FV).

What changes the result the most

• Interest rate: because it is applied repeatedly through (1 + r)^N, small rate changes compound into large differences over long horizons.
• Time (N): the exponent in the formula - the longer the horizon, the more dramatically compounding and discounting work.
• Compounding frequency: more frequent compounding on the same nominal rate slightly raises the effective return and the future value.
• Payment size and timing: larger payments obviously move the result, and beginning-of-period timing adds an extra (1 + r) of growth.
• Sign of the cash flows: getting an outflow vs. inflow wrong flips the whole problem, so confirm your signs before trusting a number.

Practical tips

• Match N to the period. Monthly compounding over 10 years is N = 120, with the annual rate divided by 12 - not N = 10.
• Keep one consistent sign rule. Treat money you pay out as negative throughout a single problem and you will rarely go wrong.
• Use the rate solver to compare offers. Turning a cash-flow stream into a single annualized rate is the cleanest way to rank financing or investment options.
• For a lump sum, set PMT to zero. Then the tool behaves as a clean present value future value calculator.

Limitations and assumptions

• It assumes a constant interest rate and equal, regularly spaced cash flows; it does not model variable rates or uneven payments.
• It ignores taxes, fees, and inflation. To see purchasing power in today's dollars, discount your FV by an inflation rate separately.
• Solving for the rate or N only works when the cash flows can mathematically reach the target; otherwise the tool reports no solution.
• It is a planning and learning tool, not personalized financial advice. Verify any decision with your own figures and a professional where appropriate.

How it compares to related calculators

This page is the general engine; sister tools focus on one corner of the same equation:

• To grow a deposit with returns, use the Future Value Calculator.
• To discount a future amount to today, use the Present Value Calculator.
• To project investing with regular contributions, use the Investment Calculator.
• To see how a single sum compounds, use the Compound Interest Calculator.
• To value or size an annuity stream, use the Annuity Calculator.

About this formula

The time-value-of-money equation is a deterministic mathematical identity, not a published rate or rule, so it does not require an external source. The single-sum and ordinary/annuity-due forms used here are the standard relationships taught in any corporate-finance course and implemented identically in financial calculators and spreadsheet functions such as FV, PV, PMT, RATE, and NPER. The rate is solved by numerical bisection because no algebraic solution exists for it - the same technique those tools use under the hood.