Finance tools
Time value of money (TVM) calculator
Free time value of money calculator and TVM calculator — enter any four of PV, FV, PMT, rate, and periods, and we solve the fifth. Deposits or withdrawals, compounding, chart, schedule, and export. Results update as you type. Related: future value calculator, present value calculator, NPV calculator. For education and planning only — not financial advice.
What is time value of money?
Time value of money (TVM) is the idea that a dollar today is worth more than a dollar in the future, because money you have now can earn interest or returns over time. That is why loans charge interest, why investors use a discount rate, and why a payment far in the future has a lower present value than the same nominal future value when the rate is positive.
Most TVM problems use five inputs: PV (amount today), FV (amount at the end), PMT (the same payment each period), rate (annual interest, converted to a rate per period), and N (how many periods). Enter any four; this calculator finds the fifth — the same logic as Excel’s FV, PV, PMT, RATE, and NPER functions.
Use the results for learning and rough planning, not as investment, tax, or legal advice.
Five solve modes
Future value, present value, payment, rate, or periods — live results.
Deposits or withdrawals
Model savings contributions or retirement withdrawals per period.
Period schedule + chart
Period-by-period schedule and a growth chart you can read on any screen.
CSV/PDF export
Download inputs and headline results for models or sharing.
TVM formulas: future value, present value, and annuity
The core time value of money formulas connect PV and FV for a lump sum, then add an annuity term when you have equal deposits or withdrawals each period:
Lump sum and annuity
FV = PV × (1 + i)n + PMT × annuity factorPV = FV / (1 + i)n (lump sum only)
Where i is the interest rate per compounding period (derived from your annual rate and compounding dropdown), and n is the number of periods. The annuity factor is ((1 + i)n − 1) / i, multiplied by (1 + i) when payments are at the beginning of each period.
Worked example (annuity + lump sum): $1,000 starting balance plus $100 deposited each period for 10 periods at 6% per year (annual compounding) → FV ≈ $3,108.93. Try the preset chips above to load this scenario instantly.
Lump-sum only: $10,000 at 6% for 10 periods (no deposits) → FV ≈ $17,908.48. Use the Lump sum 10y preset to verify.
Annuity payments in TVM (equal PMT each period)
Many TVM problems include an annuity — the same dollar amount PMT every period — on top of an optional starting lump sum PV. Loans, leases, savings plans, and pension illustrations often assume level payments.
Ordinary annuity FV
FVannuity = PMT × ((1 + i)n − 1) / iAdd lump-sum growth PV × (1 + i)n for the full balance. Set Payment mode to solve PMT when you know PV, target FV, rate, and periods — or use Future value mode when PMT is known.
Example: $100/month for 10 years (120 months) at 6% annual with monthly compounding and no starting balance → FV ≈ $16,247.34. For beginning-of-month deposits, switch payment timing to Beginning of period in the advanced panel.
Compounding frequency and periodic rates
Most savings and retirement accounts compound monthly even when you quote an annual rate. To match that in this calculator, set Compounding to Monthly and set Number of periods to total months (e.g. 120 for 10 years).
Effective periodic rate (not annual ÷ 12)
This tool uses i = (1 + r)1/m − 1 where r is the annual rate and m is periods per year (12 for monthly). That is slightly higher than r ÷ 12 and matches standard effective-rate TVM.
At 6% annual with monthly compounding, i ≈ 0.4868% per month — not exactly 0.5%.
Enter your monthly contribution as Periodic deposit (PMT) and keep payment timing at end of period unless your plan uses beginning-of-month deposits.
Example: $5,000 today plus $100/month for 120 months at 5% annual with monthly compounding → FV ≈ $23,580.79. For savings goals and side-by-side scenarios, see our compound interest calculator.
Present value: discounting future cash to today
Present value answers a simple question: what is a future amount worth in today’s dollars? Choose Present value mode, enter your target future value, rate, periods, and compounding — the calculator returns PV.
PV = FV / (1 + i)nWith equal periodic payments, the engine discounts the annuity stream using the same periodic rate i and payment timing you select.
Worked PV examples
Lump sum:$1,000 in 10 years at 6% annual compounding → PV ≈ $558.39 (preset: Present value discount).
Large receipt:$100,000 in 20 years at 12% annual → PV ≈ $10,366.68. Use Present value mode or our present value calculator preset $100k @ 12% / 20y.
This TVM page also solves payment, rate, and periods. For uneven yearly project cash flows, use our NPV calculator.
Solve for periodic payment (PMT)
Use Payment mode when you know how much you can invest today, your target ending balance, the rate, and how long you will save — but not the equal deposit each period. Classic question: “How much must I save every year to reach my goal?”
Worked example
PV = $1,000, target FV = $3,108.93, rate = 6% annual, 10 periods, annual compounding, end-of-period deposits → PMT = $100.00 per period. Switch to Payment mode and enter the four known values to verify.
In Excel: =PMT(rate, nper, pv, fv, type). For loan-style questions where PMT is the unknown payment on a fixed balance, confirm sign convention (Excel uses negative for payments out).
Solve for interest rate or number of periods
Not every TVM question starts with a known rate or horizon. Interest rate and Periods modes answer “what return do I need?” and “how long will it take?” when the other four inputs are fixed.
| Mode | You provide | Calculator solves |
|---|---|---|
| Interest rate | PV, FV, PMT, N, compounding | Annual rate % (via periodic i) |
| Periods | PV, FV, PMT, rate, compounding | Number of periods N |
Worked check at 6% over 10 periods
Rate solve: PV $1,000 + PMT $100 × 10 → FV $3,108.93 implies 6% annual (annual compounding).
Periods solve: Same inputs at 6% → 10 periods to reach $3,108.93. Rate and period solves use the same engine as FV/PV; iterative methods apply when needed.
In Excel: =RATE(nper, pmt, pv, fv, type) and =NPER(rate, pmt, pv, fv, type) with the same sign conventions as FV and PV.
Deposits vs withdrawals in TVM
Set Cash flow to Deposit when money leaves your pocket each period and adds to the balance (savings contributions, level 401(k) deferrals). Set it to Withdraw when you take money out each period while the remainder stays invested — common for retirement drawdown illustrations.
Deposit vs withdrawal examples
Deposit: PV $1,000 + PMT $100/period × 10 @ 6% annual → FV ≈ $3,108.93 (Savings + deposits preset).
Withdraw: PV $250,000, withdraw $24,000/year × 20 @ 8% → remaining FV ≈ $66,952 (Retirement withdrawal preset).
The period schedule and chart reflect the direction you select. For detailed 401(k) deferrals, match, and limits, use our 401(k) calculator.
Inflation and purchasing power (advanced)
Nominal TVM results show future dollars at your assumed interest rate. Inflation erodes purchasing power — $1 in 20 years may not buy what $1 buys today even if your account balance grew.
In Future value mode, open the advanced panel and enter an inflation rate. The results breakdown adds an inflation-adjusted FV row that restates the ending balance in today’s dollars (deflating the nominal FV by inflation over the horizon).
For CPI history, country tables, and salary purchasing-power stories, use our inflation calculator. TVM here does not model variable inflation year by year — use a single assumed rate for illustration.
TVM calculator vs other finance calculators
Not sure which calculator fits your question? Use this quick guide:
| Your question | Best tool |
|---|---|
| Solve any one of PV, FV, PMT, rate, or periods (level PMT) | This TVM calculator |
| Same five modes, focused on future value examples | Future value calculator |
| PV-first lump sum or annuity tabs | Present value calculator |
| Uneven Year 1–N project cash flows, accept/reject | NPV calculator |
| Savings compare / goal contribution stories | Compound interest calculator |
| Only start balance, end balance, and years (no PMT) | CAGR or rate of return calculator |
Future value, present value, and compound growth
Future value asks how much today’s money grows to after interest and optional equal payments. Present value runs the same math backward: what you would pay or set aside today to match a known future amount. For a lump sum at a fixed rate, they are inverses: PV = FV ÷ (1 + i)n.
Compound interest is the engine behind both — interest earned on interest. This TVM calculator handles the full five-variable setup (including solving for payment, rate, or length). A compound interest calculator is better when you want savings goal and comparison stories rather than textbook TVM solves.
When cash flows change every year (typical in project finance), step up to NPV. When you only have a start balance, end balance, and years — no level PMT — try CAGR or rate of return. For simple interest without compounding, see our simple interest calculator.
Time value of money calculator in Excel
You can replicate this time value of money calculator in Excel with five built-in functions — one for each solve mode on the mode rail above.
| Solve for | Excel function |
|---|---|
| Future value | =FV(rate, nper, pmt, pv, type) |
| Present value | =PV(rate, nper, pmt, fv, type) |
| Periodic payment | =PMT(rate, nper, pv, fv, type) |
| Interest rate | =RATE(nper, pmt, pv, fv, type) |
| Number of periods | =NPER(rate, pmt, pv, fv, type) |
Excel’s TVM functions map directly to the five solve modes on this calculator. rate must be the interest rate per period (for monthly compounding with a 6% annual quote, use 6%/12 or an equivalent effective monthly rate). nper is total periods. pmt and pv use opposite signs for money in vs out (deposits negative in Excel convention). type is 0 for end-of-period payments, 1 for beginning.
This calculator converts your annual rate to an effective periodic rate for monthly/quarterly compounding (i = (1 + r)1/m − 1), which avoids the common mistake of dividing the annual rate by 12 when compounding is monthly.
Example — FV with monthly deposits: 6% annual compounded monthly for 10 years with $100/month and $1,000 starting balance: =FV(6%/12, 120, -100, -1000, 0).
Example — PV of $1,000 in 10 years at 6% annual, no PMT: =PV(6%, 10, 0, -1000, 0) ≈ $558.39. Or use Present value mode on this page.
When to use this calculator
Use a time value of money (TVM) calculator when you know four of the five classic variables (PV, FV, PMT, rate, periods) and need the fifth:
- Savings and annuity plans — starting balance plus equal deposits (Future value or Payment mode).
- Retirement withdrawals — set Withdraw and solve remaining balance or draw amount; for 401(k) deferrals and IRS limits, use our 401(k) calculator.
- Rate or horizon checks — solve Interest rate or Number of periods when PV, PMT, and FV are known.
- Discounting — “What is $50,000 in 10 years worth today at 6%?” (Present value mode); for PV-first lump sums, see our present value calculator.
- Excel parity — match FV(), PV(), PMT(), RATE(), and NPER() with the same compounding and payment timing.
For irregular project cash flows (NPV), use our NPV calculator. Not tax or investment advice.
Limits and what this calculator does not model
This time value of money calculator is for education and planning with fixed rates and equal periodic cash flows. It is not a substitute for professional tax, legal, or investment advice.
- Variable returns — stock and fund returns change every year; TVM assumes a constant rate unless you run separate scenarios.
- Uneven cash flows — different amounts each year belong on the NPV calculator, not level-PMT TVM.
- Loan amortization schedules with changing principal/interest splits — use amortization schedule or auto loan calculator for payment breakdowns.
- Continuous compounding — not supported here; choose daily, monthly, quarterly, or annual compounding instead.
- Taxes and fees — not deducted unless you adjust inputs manually.
Always confirm account-specific rules, compounding, and payment dates with your institution or advisor.
How to use this calculator
Choose what to solve for
On the mode rail, select future value, present value, payment, interest rate, or number of periods. The field you are solving for is calculated automatically.
Enter the other four TVM inputs
Fill present value, future value, periodic payment, annual rate, and number of periods. Pick compounding frequency to match your account or assumption.
Set cash flow direction and timing
Choose deposit vs withdraw for PMT. In the advanced panel, set payment at beginning or end of period; optionally add an inflation rate for an inflation-adjusted FV row.
Review chart, schedule, and breakdown
Check the headline result, total interest, growth chart, and paginated period schedule. Use preset chips to load common textbook scenarios.
Export or share
Download CSV or PDF with inputs and results for spreadsheets, coursework, or client notes.
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Frequently asked questions about the time value of money (TVM) calculator on this page
What is time value of money?
Time value of money means a dollar today is worth more than a dollar later because money can earn interest. Investors discount future cash flows to present value; savers compound today’s balance to future value. TVM is the foundation for loans, bonds, NPV, and retirement projections.
What is a TVM calculator?
A TVM calculator (time value of money calculator) solves for any one of five linked inputs — present value, future value, periodic payment, interest rate, or number of periods — when you provide the other four. It matches finance textbooks and Excel TVM functions (FV, PV, PMT, RATE, NPER).
What is the time value of money formula?
For a lump sum: FV = PV × (1 + i)n and PV = FV / (1 + i)n. With equal periodic payments add the annuity factor: PMT × ((1 + i)n − 1) / i (adjusted for payment timing). i is the rate per compounding period; n is the number of periods.
How do you calculate time value of money?
Pick the variable you need (PV, FV, PMT, rate, or periods) and supply the other four. For a lump sum: FV = PV(1 + i)n or PV = FV / (1 + i)n. With equal deposits add the annuity factor. Use the mode rail above or match Excel FV/PV/PMT/RATE/NPER with the same periodic rate i and n.
What is the difference between TVM and NPV?
TVM here assumes level periodic payments (or none) and solves one of five variables. NPV sums uneven yearly project cash flows minus initial investment for accept/reject decisions. Use this TVM calculator for savings and textbook problems; use our NPV calculator for capital budgeting with different amounts each year.
TVM calculator vs present value calculator — which should I use?
Use the present value calculator when you mainly want a present-value layout with lump-sum and annuity discount tabs. Use this TVM calculator when you also need to solve payment, rate, or periods, or want all five modes on one page.
TVM calculator vs future value calculator — which should I use?
Both use the same five-mode calculator. Choose the future value calculator if you mainly care about growth and FV examples; stay on this page if you want TVM framing and the full time-value-of-money label with the same features.
How do you calculate periodic payment (PMT) in TVM?
Switch to Payment mode and enter PV, target FV, rate, and periods. The calculator solves PMT = (FV − PV(1 + i)n) / annuity factor. Use Withdraw for retirement drawdowns (e.g. $24,000/year from a $250,000 portfolio).
How do you solve for interest rate in TVM?
Select Interest rate mode and enter PV, FV, PMT, and periods. The calculator solves for the periodic rate that connects your inputs, then converts it to an annual nominal rate for your compounding frequency. In Excel, use =RATE(nper, pmt, pv, fv, type).
How do you solve for number of periods in TVM?
Select Number of periods mode and enter PV, FV, PMT, and rate. The calculator finds how many compounding periods match your goal balance. In Excel, use =NPER(rate, pmt, pv, fv, type) with the same periodic rate and payment sign convention as FV and PV.
How much will $10,000 be worth in 30 years?
With no further deposits, annual compounding, and end-of-period timing: FV = 10,000 × (1 + r)30. At 7% per year, FV ≈ $76,122.55. At 5%, FV ≈ $43,219.42. Enter PV = 10000, PMT = 0, rate, periods = 30, and compounding = Annually above to verify any assumption.
What is the future value formula?
For a lump sum: FV = PV × (1 + i)n. With equal periodic deposits: add PMT × ((1 + i)n − 1) / i (times (1 + i) if payments are at the beginning of each period). i is the rate per compounding period; n is the number of periods.
How do you calculate future value with monthly deposits?
Set Compounding to Monthly, enter your monthly deposit as Periodic deposit (PMT), and set Number of periods to total months (e.g. 120 for 10 years). The calculator uses an effective monthly rate i = (1 + r)1/12 − 1 (not annual rate ÷ 12), then applies FV = PV(1 + i)n + PMT × annuity factor with your payment timing.
What is the difference between future value and present value?
Future value projects today’s money forward with interest. Present value discounts a future amount back to today. They are inverse operations: PV = FV / (1 + i)n for a lump sum. Use the mode rail above to switch solves.
TVM vs compound interest calculator — when to use which?
Use this TVM calculator when you need to solve for payment, rate, or periods as well as PV or FV, or when you want Excel-style TVM functions. Use our compound interest calculator for savings goals, comparisons, and contribution-focused walkthroughs. Both model growth; the difference is which questions each page is built around.
What does payment at beginning vs end of period mean?
End of period (ordinary annuity) assumes deposits after interest accrues for that period — typical for many savings accounts. Beginning of period (annuity due) assumes deposits before interest — common for rent or some payroll savings. Beginning timing yields a slightly higher FV.
How do compounding periods affect future value?
More frequent compounding (e.g. daily vs annual) increases FV for the same nominal annual rate because interest earns interest sooner. Select the frequency that matches your account or assumption in the compounding dropdown.
How do you calculate time value of money in Excel?
Excel’s TVM functions mirror this calculator: =FV(rate, nper, pmt, pv, type), =PV(rate, nper, pmt, fv, type), =PMT(rate, nper, pv, fv, type), =RATE(nper, pmt, pv, fv, type), and =NPER(rate, pmt, pv, fv, type). Use the same periodic rate and nper as your compounding (e.g. 6%/12 and 120 for monthly over 10 years). Example FV: 6% annual, monthly compounding, $100/month, $1,000 starting balance → =FV(6%/12, 120, -100, -1000, 0).
Does this calculator account for inflation?
Optionally. Open the advanced panel and enter an inflation rate to see an inflation-adjusted FV row in the results breakdown. For full CPI history or purchasing-power tables, use our inflation calculator.
What is the future value of $1,000 invested for 20 years at 8%?
With annual compounding, no further deposits, and end-of-period timing: FV = 1,000 × (1.08)20 ≈ $4,660.96. Enter PV = 1000, PMT = 0, rate = 8%, periods = 20, compounding = Annually in the calculator above to verify.
What is the present value of $1,000 in 10 years at 6%?
With annual compounding and no periodic deposits: PV = 1,000 / (1.06)10 ≈ $558.39. Switch to Present value mode here, or use our dedicated present value calculator for lump sum and annuity discounting.
What is the future value of $5,000 in 10 years at 5% compounded monthly?
With no further deposits: set PV = 5000, PMT = 0, rate = 5%, periods = 120, compounding = Monthly. FV ≈ $8,144.47 (effective monthly rate i = (1 + r)1/12 − 1). This calculator uses effective periodic rates, not a simple annual rate ÷ 12.
What is the future value of an annuity?
It is the FV of a series of equal payments (PMT) at a fixed rate. Formula: PMT × ((1 + i)n − 1) / i, adjusted for payment timing. Enter your deposit amount as PMT and set periods to match your schedule.
How do you calculate present value?
For a lump sum: PV = FV / (1 + i)n, where i is the rate per compounding period and n is the number of periods. Switch to Present value mode above, or use our present value calculator for lump-sum and annuity discount tabs.
What is the present value of $5,000 in 10 years at 10%?
With annual compounding and no periodic deposits: PV = 5,000 / (1.10)10 ≈ $1,927.72. Verify in Present value mode here or on our present value calculator.
What is the present value of $100,000 in 20 years at 12%?
Discounting a single future receipt with annual compounding: PV = 100,000 / (1.12)20 ≈ $10,366.68. Use Present value mode with FV = 100000 here, or the present value calculator preset $100k @ 12% / 20y.
What is the future value of $800 at 8% after 6 years?
Lump sum with annual compounding and no deposits: FV = 800 × (1.08)6 ≈ $1,269.50. Enter PV = 800, PMT = 0, rate = 8%, periods = 6, compounding = Annually.
What is the future value of $1,500 at 5% for 7 years?
With no further deposits and annual compounding: FV = 1,500 × (1.05)7 ≈ $2,110.65. Enter PV = 1500, PMT = 0, rate = 5%, periods = 7 in Future value mode.
Can this TVM calculator model withdrawals?
Yes. Set Cash flow to Withdraw and enter the amount withdrawn each period as PMT. Use Future value mode to see the remaining balance (e.g. $250,000 starting balance, $24,000/year withdrawn for 20 years at 8% → FV ≈ $66,952). Load the Retirement withdrawal preset to try this scenario.
What is the difference between deposits and withdrawals in TVM?
Deposits add equal amounts to the balance each period (savings contributions). Withdrawals remove equal amounts while the rest stays invested (drawdown illustrations). Choose Deposit (add money) or Withdraw in the Cash flow dropdown above — enter a positive PMT amount; you do not need to type negative payments manually.
Is this financial advice?
No. Results are illustrative estimates for education and planning. Actual returns vary with markets, fees, taxes, and account rules. Consult a qualified professional for investment or tax decisions.