Finance Calculator

Live five-key time-value-of-money board for FV, PV, PMT, rate per period, and N, with a begin ↔ end timing twin and period-path strip.

Educational TVM sketch only. Not investment, loan, tax, or product advice. Confirm quotes with a lender or advisor.

By Ahmet C. Toplutaş·Site owner & editor · Finance tools

Last updated May 21, 2026 · Reviewed May 21, 2026 · Planning estimates only - not tax, medical, or investment advice

Five-key TVM solve

A classic finance calculator links five keys: FV, PV, PMT, rate per period, and N. Enter any four and solve for the fifth.

This page's framing is that five-key hub, with a begin ↔ end timing twin, a sign peel, and a period-path strip. It is not the compound-interest drip/frequency board, not the loan interest-tax ladder, and not the investment fee-drag bridge.

Decision framing: “Which TVM key is missing, and do payments land at the end or beginning of each period?”

Educational TVM sketch only. Not investment, loan, tax, or product advice. Confirm quotes with a lender or advisor. See our disclaimers.

Begin ↔ end timing twin

End (ordinary) assumes level payments at the end of each period. Begin (annuity due) assumes payments at the start. When PMT is non-zero, the twin recomputes the solved key under the other timing so you can see the gap.

Tip: load Annuity due, then flip to End timing and watch FV drop on the twin.

Cash-flow sign peel

This literacy board often treats positive PV as money already invested and positive PMT as a deposit. Loan payment solves can return a negative PMT in the savings-equation orientation (outflow). Read the magnitude as the payment size, then hand off to a loan schedule board when you need amortization detail.

Period-path strip

The strip evaluates the same PV, PMT, rate, and timing at about 25%, 50%, 75%, and 100% of N. Use it to see how a running future-value sketch builds before the final key.

Core relations

Ordinary (end) identities; begin multiplies the annuity factor by (1 + r).

FV = PV(1+r)^N + PMT × ((1+r)^N − 1) / r (end, r ≠ 0) begin annuity factor ≈ ordinary × (1+r) r = rate per period (match N’s unit) PMT = (FV − PV(1+r)^N) × r / ((1+r)^N − 1)

Example: PV $10,000, PMT $200, r = 7%/yr, N = 10, end timing → FV on the nest-egg preset. Rate must be per period: monthly stories use monthly r and months for N.

Where this hands off

Sibling boards when you need schedules, frequency drip, or fee drag.

Compound interest (drip vs lump, compounding frequency)
Loan / payment
Investment (fee-drag and contribution stack)
Terms: finance glossary

Worked scenarios

Scenario A: Nest egg. Solve FV with PV $10,000, annual deposits $200, 7%, 10 years, end timing. Path strip shows growth along N.

Load Discount PV: FV $15,000 in 5 years at 6% with PMT 0 → present value of a lump.

Scenario B: Loan PMT. PV $25,000, FV 0, 0.5% per month, N = 60. Solved PMT may be negative (outflow); use the magnitude as the monthly payment sketch.

Scenario C: Annuity due. Begin timing with level deposits. Flip to end on the twin to quantify the due premium.

Scenario D: Need a schedule. Hand off to loan or compound boards once the TVM keys are closed.

Common mistakes

Mixing annual rate with monthly N (rate must match the period).
Ignoring begin vs end when payments are large relative to PV.
Treating a negative PMT as a software bug instead of an outflow sign.
Using this hub instead of compound interest when frequency drip is the whole question.
Expecting taxes, fees, or credit decisions inside a TVM sketch.

How to use this board

Choose which key to solve: FV, PV, PMT, rate, or N.
Enter the other four knowns; match rate units to N.
Pick end (ordinary) or begin (due) timing.
Read the closed keys, timing twin, and period-path strip.
Share writes board state; typing does not rewrite the address bar.

When not to stop at this sketch

Stop here for general TVM literacy and begin/end intuition. Hand off for amortization schedules, compounding-frequency experiments, or fee-aware investing. For real offers, use lender disclosures and professional advice.

Compounding frequency: compound interest calculator.
Loan schedules: loan calculator.
Fee drag: investment calculator.

Frequently asked questions

How does this finance calculator work?

It is a five-key time-value-of-money board. Choose what to solve (FV, PV, PMT, rate per period, or N), enter the other knowns, and pick end (ordinary) or begin (annuity due) timing. A begin ↔ end twin shows the gap when payments exist, and a period-path strip sketches value along N.

What is the begin ↔ end timing twin?

End timing compounds level payments as an ordinary annuity (end of each period). Begin timing treats payments as annuity due (start of each period), which usually grows a savings FV faster or changes loan PMT. The twin recomputes the solved cash-flow key under the other timing.

Is the interest rate annual or per period?

Rate is per period, matched to N. For monthly loans, enter monthly rate (APR/12 as a sketch) and N in months. For annual compounding stories, use annual rate and years.

What do the cash-flow signs mean?

This literacy board often uses positive PV as money already in the account and positive PMT as a deposit. Loan payment solves can return a negative PMT in the savings-equation orientation (cash outflow). Read the magnitude as the payment size.

How is this different from compound interest or loan calculators?

Compound interest focuses on drip vs lump and compounding frequency. Loan and EMI boards focus on amortization schedules. This page is the general TVM solve hub with begin/end timing.

What is the period-path strip?

It evaluates the same PV, PMT, rate, and timing at 25%, 50%, 75%, and 100% of N so you can see how the running future value sketch builds.

Is this financial advice?

No. It is an educational TVM sketch only. Not investment, loan, tax, or product advice. Confirm quotes with a lender or advisor. See our disclaimers.

Sources

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Methodology & sources

Our finance calculators use standard formulas and common assumptions. Results are estimates and may differ due to fees, taxes, rounding, and lender/provider policies. Use this for planning—not as a quote.

Core sources

Finance calculators Finance formulas Editorial policy Corrections Contact

Five-key TVM solve

A classic finance calculator links five keys: FV, PV, PMT, rate per period, and N. Enter any four and solve for the fifth.

Decision framing: “Which TVM key is missing, and do payments land at the end or beginning of each period?”

Educational TVM sketch only. Not investment, loan, tax, or product advice. Confirm quotes with a lender or advisor. See our disclaimers.

Cash-flow sign peel

Core relations

Ordinary (end) identities; begin multiplies the annuity factor by (1 + r).

FV = PV(1+r)^N + PMT × ((1+r)^N − 1) / r (end, r ≠ 0) begin annuity factor ≈ ordinary × (1+r) r = rate per period (match N’s unit) PMT = (FV − PV(1+r)^N) × r / ((1+r)^N − 1)

Example: PV $10,000, PMT $200, r = 7%/yr, N = 10, end timing → FV on the nest-egg preset. Rate must be per period: monthly stories use monthly r and months for N.

Worked scenarios

Scenario A: Nest egg. Solve FV with PV $10,000, annual deposits $200, 7%, 10 years, end timing. Path strip shows growth along N.

Load Discount PV: FV $15,000 in 5 years at 6% with PMT 0 → present value of a lump.

Scenario B: Loan PMT. PV $25,000, FV 0, 0.5% per month, N = 60. Solved PMT may be negative (outflow); use the magnitude as the monthly payment sketch.

Scenario C: Annuity due. Begin timing with level deposits. Flip to end on the twin to quantify the due premium.

Scenario D: Need a schedule. Hand off to loan or compound boards once the TVM keys are closed.

Common mistakes

Mixing annual rate with monthly N (rate must match the period).
Ignoring begin vs end when payments are large relative to PV.
Treating a negative PMT as a software bug instead of an outflow sign.
Using this hub instead of compound interest when frequency drip is the whole question.
Expecting taxes, fees, or credit decisions inside a TVM sketch.

When not to stop at this sketch

Compounding frequency: compound interest calculator.
Loan schedules: loan calculator.
Fee drag: investment calculator.

Frequently asked questions

How does this finance calculator work?

What is the begin ↔ end timing twin?

Is the interest rate annual or per period?

Rate is per period, matched to N. For monthly loans, enter monthly rate (APR/12 as a sketch) and N in months. For annual compounding stories, use annual rate and years.

What do the cash-flow signs mean?

How is this different from compound interest or loan calculators?

Compound interest focuses on drip vs lump and compounding frequency. Loan and EMI boards focus on amortization schedules. This page is the general TVM solve hub with begin/end timing.

What is the period-path strip?

It evaluates the same PV, PMT, rate, and timing at 25%, 50%, 75%, and 100% of N so you can see how the running future value sketch builds.

Is this financial advice?

No. It is an educational TVM sketch only. Not investment, loan, tax, or product advice. Confirm quotes with a lender or advisor. See our disclaimers.

Five-key TVM solve

Begin ↔ end timing twin

Cash-flow sign peel

Period-path strip

Core relations

Where this hands off

Worked scenarios

Common mistakes

How to use this board

When not to stop at this sketch

Frequently asked questions

How does this finance calculator work?

What is the begin ↔ end timing twin?

Is the interest rate annual or per period?

What do the cash-flow signs mean?

How is this different from compound interest or loan calculators?

What is the period-path strip?

Is this financial advice?

Sources

Methodology & sources

Five-key TVM solve

Begin ↔ end timing twin

Cash-flow sign peel

Period-path strip

Core relations

Where this hands off

Worked scenarios

Common mistakes

How to use this board

When not to stop at this sketch

Frequently asked questions

How does this finance calculator work?

What is the begin ↔ end timing twin?

Is the interest rate annual or per period?

What do the cash-flow signs mean?

How is this different from compound interest or loan calculators?

What is the period-path strip?

Is this financial advice?

Sources

What this number means

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