Time Value of Money Calculator
This time value of money (TVM) calculator solves the core savings equation from any direction. Pick the variable you want to find — the future value of a plan, the starting amount you'd need today, the monthly payment that gets you to a goal, or how long the goal will take — then fill in the other numbers and the answer appears instantly.
The time value of money is the idea that a dollar today is worth more than a dollar tomorrow, because today's dollar can be invested and grow. It's the concept underneath almost every financial decision: retirement planning, saving for a house, comparing a lump sum to installments. This solver lets you ask the question whichever way your situation frames it.
How it works
All four modes use the same underlying relationship between a starting amount (present value), a regular monthly payment, an interest rate, and time. The calculator assumes monthly compounding and payments made at the end of each month (an ordinary annuity), with every amount entered as a positive number. Choose what to solve for, and the calculator rearranges the equation to isolate that variable — the input you're solving for is grayed out since it's the answer, not an ingredient.
Formula
With monthly rate i (annual rate ÷ 12) and n months, the future value is FV = PV(1 + i)n + PMT × ((1 + i)n − 1) / i. Solving for present value or payment rearranges this directly. Solving for time uses logarithms: n = ln((FV·i + PMT) / (PV·i + PMT)) / ln(1 + i). At a 0% rate the equation collapses to simple addition: FV = PV + PMT × n.
Worked example
Suppose you want $100,000 in 10 years, you have $10,000 today, and you expect a 6% annual return. Solving for the monthly payment: your $10,000 grows to about $18,194 on its own, leaving $81,806 for contributions to cover. The required payment works out to about $499 per month. Solve for years instead with a $200 payment and the same goal takes about 17.2 years — a concrete picture of the trade-off between saving more and waiting longer.
This calculator is for informational purposes only, not professional advice. Projections assume a constant rate of return and ignore taxes, fees, and inflation. Consult a qualified financial advisor before making investment decisions.
Frequently asked questions
What is the time value of money?
The time value of money is the principle that money available now is worth more than the same amount later, because it can be invested and earn a return in the meantime. It is why lenders charge interest, why investors discount future cash flows, and why starting to save early matters so much. Every mode of this calculator is a different rearrangement of that one idea.
Which variable should I solve for?
Solve for future value to see where a savings plan ends up. Solve for present value to find the lump sum you would need today to hit a goal — useful for comparing a windfall against a payment plan. Solve for monthly payment when you have a target and a deadline and need to know what it costs each month. Solve for years when your budget is fixed and you want to know how long the goal takes.
Why are payments assumed at the end of each month?
Payments at the end of each period form an ordinary annuity, the standard convention for loans and most savings plans. The alternative — payments at the start of each period, called an annuity due — gives each contribution one extra month of growth, producing a slightly higher future value. The difference is roughly the monthly interest rate applied to your contributions, usually under 1% of the final balance.
What interest rate should I use?
Match the rate to where the money will actually sit. High-yield savings accounts have recently paid around 4-5%, and diversified stock index funds have historically averaged about 7-10% annually before inflation, with substantial year-to-year swings. For discounting future money back to today, many planners use a rate between a safe bond yield and expected market returns. When in doubt, run the calculation with a conservative and an optimistic rate to bracket the answer.
Why can I not solve for the interest rate?
Unlike the other variables, the interest rate cannot be isolated algebraically — finding it requires iterative numerical methods, and the answer can be misleading when a goal is unreachable at any reasonable rate. To keep results transparent, this calculator solves the four closed-form variables. If you need the implied rate, try a few rates in future-value mode and narrow in on the one that hits your target.
How is this different from the compound interest calculator?
The compound interest calculator works forward only: you supply the starting amount, rate, and time, and it projects the ending balance, with a choice of compounding frequencies. This TVM solver works in any direction — it can start from the goal and tell you the required deposit, payment, or timeline. Use the compound interest tool to explore growth, and this one when you have a target to hit.