Financial Calculator — Solve PV, FV, Payment, Rate & Time (TVM)
The time value of money, in one solver. Enter the present value, payment, rate and time you know, choose what to solve for, and get the missing number — with the growth curve that shows how the balance builds.
The knowns — and the unknown
Advanced options — payments per year, compounds per year & payment timing
Payments per year and payment timing are already included in the result with their default values — open Advanced options to change them.
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The answer
- One equation, five variables: FV = PV grown + payments grown — solve for whichever one you leave out. Four come out with algebra or logarithms; the rate is found by iteration.
- The worked example — $10,000 plus $100 a month at 7% for 10 years — grows to $37,405.09, of which only $22,000.00 came out of a pocket; the other $15,405.09 is interest.
- Beginning-of-period payments are worth more: the same plan with payments at the start of each period grows to $37,506.06.
The time value of money, in one solver. Enter the present value, payment, rate and time you know, choose what to solve for, and get the missing number — with the growth curve that shows how the balance builds.
The balance, building
The growth curve for the current scenario, period by period — the starting amount compounding, with each payment landing on top. Curves bend upward because interest starts earning interest. The schedule under the chart writes the same build-up out in numbers, one row per period.
| Period | Payment | Interest | Balance |
|---|
One row per period: the payment that lands, the interest the balance earns that period, and the balance at the period’s end.
Keep exploring
Three companion tools for growing money.
How it works
Three steps from question to answer.
Pick the unknown
Choose what to solve for — future value, present value, the payment, the interest rate, or the time it takes. That field becomes the answer.
Enter the knowns
The amounts, the annual rate, the years, how many payments land each year, and whether each payment is made at the start or the end of its period.
Read the breakdown
The solved value, how much of it is your starting amount grown, how much is your payments grown, and how much is pure interest.
The math behind the time value of money
Money today and money later are different amounts, because today’s money earns interest. With a periodic rate i (annual rate ÷ payments per year) and n periods (years × payments per year), a present value grows by the factor (1 + i)n, and a level payment made every period grows into an annuity worth PMT × [((1 + i)n − 1) ÷ i] — multiplied by one extra (1 + i) when payments land at the beginning of each period instead of the end. Future value is simply the two grown pieces added together, and the same equation can be rearranged to solve for the present value or the payment. Time is recovered with logarithms: divide both sides until (1 + i)n stands alone, then take logs. The interest rate is the one variable with no such rearrangement — so this solver finds it by iteration instead: it brackets the rate between two guesses and keeps halving the gap until the future value lands on your target.
Worked examples:
| Question | Calculation | Answer |
|---|---|---|
| FV: $10,000 + $100/mo · 7% · 10 yrs · monthly · end | $10,000 grows to $20,096.61 · payments grow to $17,308.48 | FV $37,405.09 |
| Payment: reach $50,000 · start $5,000 · 8% · 15 yrs · monthly · end | $5,000 grows to $16,534.61 · the $33,465.39 gap ÷ annuity factor 346.04 | Payment $96.71/mo |
| FV with beginning timing: same as row 1, payments at period start | Payments grow to $17,308.48 × 1.00583 = $17,409.45 · start still $20,096.61 | FV $37,506.06 |
Notice the split in row 1: of the $37,405.09, only $22,000.00 ever came out of a pocket — $10,000 at the start and $100 × 120 payments. The other $15,405.09 is interest: money the money earned.
Five variables, one rule
Present value, future value, payment, rate and time — enter any four and the fifth is the answer.
This page is a finance calculator — a solver built around the five variables of the time value of money. Present value (PV) is the amount on the table today. Future value (FV) is what money becomes later. Payment (PMT) is the level amount that moves every period. The rate is the annual interest, and the time is how many years the money sits. Every savings plan, loan and investment question is some combination of these five numbers.
The one rule that governs all of it: the five variables are locked together by a single equation (shown in the math section above), so if you know any four, the fifth is determined. This solver turns that rule into modes — tell it which variable is the unknown, enter the other four, and it rearranges the equation for you. It works in a positive savings convention — amounts are money in one pot, all positive — so there are no negative cash-flow signs to juggle. Use this finance calculator online whenever a money question has a “how much”, “how long” or “what would it take” shape — it runs entirely in your browser, with no sign-up and nothing to install.
Worked examples: one for every variable
Each example is solved by its formula and checked against the solver itself — the answers agree.
Solving for present value: the deposit that hits a target
You need $10,000 exactly five years from now, and an account pays 6% a year. What single deposit today lands on the target? Present value runs the growth factor backwards: PV = FV ÷ (1 + r)n = $10,000 ÷ 1.065 = $10,000 ÷ 1.3382 = $7,472.58. The remaining $2,527.42 of the target is never deposited at all — it is the interest the deposit earns along the way. That is the discounting direction of the one rule: money promised later is worth less than money in hand, and the rate and the wait decide exactly how much less. In the solver: Solve for Present Value, payments per year 1, payment 0, future value $10,000, 6%, 5 years — it returns the same $7,472.58.
Solving for future value: what a lump sum becomes
Deposit $5,000 today at 7% a year and leave it alone for ten years. Future value compounds the deposit forward: FV = PV × (1 + r)n = $5,000 × 1.0710 = $5,000 × 1.9672 = $9,835.76. Almost half of that — $4,835.76 — is interest, and the interest share grows with time because each year’s interest itself starts earning interest. Compounding frequency moves the answer slightly: the same deposit compounded monthly at a nominal 7% ends a little higher, which is why the solver asks how many periods fall in each year. Future value is the solver’s default mode — enter a $5,000 present value, zero payment, 7% and 10 years, and it returns $9,835.76.
Solving for the payment: the loan worked end to end
Run as a loan finance calculator, the payment mode answers the borrower’s version of the question. Borrow $20,000 over five years at 8% a year, paid monthly. The amortization formula spreads the principal across 60 payments, each one part interest and part principal: PMT = $20,000 × (0.08 ÷ 12) ÷ (1 − (1 + 0.08 ÷ 12)−60) = $405.53 a month. Over the term those payments add to $24,331.67 — the $20,000 borrowed plus $4,331.67 of interest, a split the cost-of-credit passage below reads in full. In the solver, enter a present value of $20,000 and a future value of $0 and solve for the payment — the magnitude it returns is the same $405.53.
Solving for the rate: iteration, and the lump-sum shortcut
The rate is the one variable no formula can reach once a payment is in the mix — it hides inside both the growth factor and the annuity factor at once. So the solver finds it the way dedicated financial calculators do: by iteration. It tests a rate, checks the future value that rate produces, and keeps narrowing — halving the gap between a rate that lands short and one that overshoots — until the future value matches yours. Try it on this page’s own default plan with a bigger target: $10,000 plus $100 a month needs to reach $50,000 in ten years. Solve for Interest Rate and the solver returns 10.62% a year — the 7% default only reaches $37,405.09, so the target demands a much hotter rate. One case does have a closed formula: a single lump sum with no payments. There the growth equation isolates cleanly: r = (FV ÷ PV)1/n − 1. If $5,000 grew to $8,000 in eight years, the rate was (8,000 ÷ 5,000)1/8 − 1 = 6.05% a year — check it forwards and $5,000 × 1.06058 lands back on $8,000, and the solver’s rate mode returns the same 6.05% for exactly those inputs.
Solving for time: how long to double
How long does $5,000 take to become $10,000 at 7% a year, with nothing added? Time comes out of the growth equation with logarithms: n = ln(FV ÷ PV) ÷ ln(1 + r) = ln(2) ÷ ln(1.07) = 10.24 years. Notice how this locks together with the future-value example above: at exactly ten years the deposit has reached $9,835.76 — close to double, but not quite — and the extra 0.24 of a year, roughly three months, closes the gap. In the solver, Number of Years mode returns 10.24 for exactly these inputs.
Principal today, and the cost of credit
Two everyday names for pieces of the same equation — and how to read both off the worked examples.
Lenders and savers both talk about the principal: the sum everything else is calculated from. At the start of a loan it is the amount borrowed; at the start of a savings plan it is the deposit. In time-value terms the principal is simply the present value — which is why this page’s present-value mode works as a principal calculator: give it the target, the rate and the time, and it tells you the principal you need on the table today, like the $7,472.58 that grows into $10,000 in the first worked example.
The cost of credit is the other figure borrowers actually feel: not the rate, but the total interest paid across the whole term. It needs no new formula — it is the payments added up, minus the principal: payments × number of payments − principal. On the loan example above that is $405.53 × 60 − $20,000 = $4,331.67. Read this way, the payment mode doubles as a cost of credit calculator: solve for the payment, multiply by the number of payments, subtract what you borrowed, and you are holding the true dollar price of the borrowing — the number worth comparing when two loan offers trade a lower rate against a longer term.
Go deeper
The timing switch, and how the solver finds the one variable no formula can isolate.
The same payment is worth more when it lands earlier, because it starts earning interest sooner:
- End of period (ordinary annuity): each payment is made at the end of its period — the pattern for loan payments and most salary-based saving.
- Beginning of period (annuity due): each payment lands at the start, so every single one earns exactly one extra period of growth — the whole payments stream is worth (1 + i) times as much.
- The default scenario shows it: switching $100 a month at 7% from end to beginning lifts the payments’ grown value from $17,308.48 to $17,409.45 — about $101 of extra interest from timing alone.
- Which should you use? Rent and many lease payments are beginning-of-period; mortgage payments and typical monthly investments are end-of-period.
No formula isolates it — so the solver iterates, the way dedicated financial calculators do:
- Four of the five variables rearrange cleanly: FV, PV and PMT come out with algebra, and time comes out with logarithms.
- The rate does not: with a payment in the mix, the rate sits inside both (1 + i)n and the annuity factor at once, and no formula isolates it.
- So the solver brackets and refines: it starts with a low rate whose future value falls short of your target and a high rate that overshoots, then keeps testing the middle rate and halving the gap until the future value matches your target to the cent.
- For a lump sum with no payments, the rate also has a closed formula — (FV ÷ PV)1/n − 1 — and the solver’s answer agrees with it: $5,000 growing to $8,000 in eight years solves to 6.05% a year either way.
Excel functions that mirror the five keys
Every key on this page has a spreadsheet twin with the same sign convention. If the two disagree, one of them has the timing or the sign wrong.
The five keys solve one equation, and Excel’s financial functions solve the same equation in cell form. PMT is the payment key: =PMT(6%/12, 360, -200000) returns $1,199.10, the monthly payment on a $200,000 loan at 6% over 30 years — the loan amount is negative because it is money received, and the payment comes back positive. FV is the future-value key: =FV(5%/12, 120, -200, 0, 0) returns $31,056.46 for $200 a month at 5% for 10 years, payments at the end of each month. PV runs the same formula backwards, RATE solves for the interest rate when the other four are known, and NPER solves for the time — the two keys this calculator finds by iteration, because no closed formula isolates them in the general case. In every function the arguments keep the same order and the same meaning: rate per period first, number of periods second, payment third, present value fourth, and the timing switch (0 for end of period, 1 for beginning) last.
NPV and IRR need a different pair, because they price an uneven stream rather than a level payment. Excel’s NPV discounts every value by one period, so the initial outlay stays outside the function: for a project costing $10,000 today and returning $3,000 a year for four years plus $4,000 in year five, =NPV(8%, 3000, 3000, 3000, 3000, 4000) – 10000 returns $2,658.71 — the net present value at an 8% discount rate, positive, so the project clears its hurdle. IRR is the discount rate that makes that same expression zero: =IRR(values) on the full stream including the initial outlay returns 17.23%, the rate at which NPV is exactly zero. The two answers agree here, as they must when the cash flows change sign only once: NPV positive at the hurdle rate and IRR above the hurdle rate are the same verdict in two languages. Where they can disagree — streams that change sign more than once, or projects of very different scale — the NPV verdict at the stated discount rate is the one to trust, and the companion guide on yield, IRR, and NPV works both cases step by step.
Frequently asked questions
Quick answers about time-value-of-money solving.
What is a financial calculator used for?
It solves time-value-of-money problems: the questions where money, interest and time trade against each other. What will my savings grow to? What must I deposit today to hit a target? What monthly payment reaches my goal? How long until I get there? Enter the four values you know and it solves for the fifth.
What does the positive savings convention mean?
Classic financial calculators treat money you pay out as negative and money you receive as positive, which forces awkward sign juggling. This solver instead imagines one savings pot: the present value and every payment go in as positive amounts, and the future value is the positive total the pot grows to. Same mathematics, no sign errors.
How is future value calculated?
In two pieces. The present value compounds for all n periods: PV × (1 + i)^n. The payments form an annuity: PMT × [((1 + i)^n − 1) ÷ i], with one extra (1 + i) factor if payments are made at the beginning of each period. In the default example, $10,000 grows to $20,096.61 and 120 payments of $100 grow to $17,308.48, giving a future value of $37,405.09.
What is the difference between end and beginning payment timing?
End-of-period payments (an ordinary annuity) land at the end of each period, like a mortgage payment. Beginning-of-period payments (an annuity due) land at the start, like rent — so each one earns one extra period of interest, and the payments stream is worth exactly (1 + i) times more. In the default scenario the difference is about $101 over ten years.
Can this calculator solve for the interest rate?
Yes — set “Solve for” to Interest Rate. When a regular payment is involved, the rate cannot be isolated by algebra or logarithms, so the solver finds it by numerical iteration: it brackets the rate between a guess that lands short and one that overshoots, then keeps halving the gap until the future value matches your target. For the default plan with a $50,000 target instead — $10,000 plus $100 a month for ten years — the rate it finds is 10.62% a year.
How do I find how long it takes to reach a savings goal?
Set “Solve for” to Number of Years, enter your target as the future value, your starting amount as the present value, your regular payment and the rate. The solver recovers the time using logarithms. For example, $10,000 plus $100 a month at 7.00% takes about 13.0 years — roughly 156 monthly payments — to reach $50,000.
What does a financial calculator solve that a loan calculator does not?
A loan calculator runs a single fixed pattern: borrow a principal, pay it down month by month until the balance reaches zero. A financial calculator solves the whole time-value-of-money equation, for whichever variable is unknown — the future value of savings, the present value you must deposit today, the payment that reaches a goal, or the time it takes to get there. Borrowing is just one corner of that bigger question.
What is the difference between present value and future value?
Present value is a future amount translated into today’s money — discounted. Future value is a present amount translated into future money — compounded. They are the same sum seen from two ends of the timeline: at 6%, $7,472.58 on the desk today and $10,000 arriving in five years are worth exactly the same, which is why the present-value example above solves for $7,472.58.
Can I solve for the interest rate if I know the payment and the term?
Yes — that is exactly what the Interest Rate mode is for. Once a regular payment is involved, the rate sits inside the equation in a way no formula can isolate, so the solver finds it by numerical iteration, bracketing and refining until the future value matches. For a lump sum with no payments there is also a closed formula: rate = (FV ÷ PV)^(1/n) − 1 — $5,000 growing to $8,000 in eight years implies 6.05% a year, and the solver returns the same 6.05% for those inputs.
What is the cost of credit, and how is it different from the interest rate?
The interest rate is a percentage — the price of borrowing per year. The cost of credit is a dollar amount: every dollar of interest you will pay over the whole term, worked out as payments × number of payments − principal. On the loan example above — $20,000 at 8% over five years — the rate reads 8%, but the cost of credit is $4,331.67, the figure that tells you what the borrowing actually takes out of your pocket.
What is the difference between a financial calculator and a scientific calculator?
A scientific calculator evaluates expressions; a financial calculator solves the time-value equation. Give a scientific calculator the formula and it will compute it — give a financial calculator any four of the five variables (N, I/Y, PV, PMT, FV) and it finds the fifth, including the two variables no formula isolates directly. A scientific calculator also has no sign convention for money in and money out, no payment-timing switch, and no cash-flow functions for NPV and IRR, so pricing a bond or a project on one means building the whole schedule by hand. For single calculations the scientific route is fine; for anything with a payment stream, the financial calculator — or its Excel twins, PMT, FV, NPV, and IRR — is the tool that keeps the timing and the signs straight.
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Disclaimer
This calculator is for information only and is not financial advice. It assumes a single constant interest rate, payments that never change, and no taxes, fees, inflation or missed payments — real accounts and investments vary in all of those. Figures are exact solutions to the formulas shown, rounded for display; use them for planning, and check product terms before committing money.