Finance Calculator: PV, FV, PMT, Rate, and N

Use this finance calculator to solve common time value of money problems by finding one unknown: present value (PV), future value (FV), payment (PMT), interest rate, or number of periods (N). It also helps you match the interest rate to your period and shows a short schedule so you can check your work.

Solve for

Scenario type

Savings / investing Use positive PV for the starting savings balance and positive PMT for deposits. FV is the resulting balance.

Loan Use positive PV for the outstanding loan and negative PMT for repayments. FV is the remaining balance.

Payment timing

End of period Interest happens first, then the payment (ordinary annuity).

Beginning of period Payment happens first (annuity due). You earn or avoid 1 extra period of interest.

Present value PV (USD)

Payment each period PMT (USD per payment)

Number of periods N (periods)

Interest rate (percent per year)

Future value FV (USD)

Advanced options

Rate and periods

Payments per year P/Y (payments per year)

Compounds per year C/Y (compounds per year)

Interest rate type

Schedule display

Schedule rows to show (rows)

Rounding for schedule cents

Solved value (the field you chose)

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Balance convention: savings start with positive PV and deposits use positive PMT. Loans start with positive PV and repayments use negative PMT. FV is the remaining balance.

Interest rate per payment period

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This is the rate that matches N (your number of payment periods), shown to at most four decimal places. Smaller nonzero rates use scientific notation. Calculations keep the full rate.

Total paid in (sum of payments)

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This is PMT times N, with sign preserved.

Total interest (approx)

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Computed from a schedule. Rounding choice can change totals by a few cents.

Ending balance after N periods

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This is the full-precision TVM equation result. If a cents-rounded schedule differs, the reconciliation appears below.

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How to use our Finance Calculator (PV, FV, PMT, Rate, N)

Choose Solve for to pick the number you want to find (PV, FV, PMT, interest rate, or N).
Pick a Scenario type: Savings / investing (you pay in now and/or each period, then receive FV) or Loan (you receive PV now, then pay PMT).
Set Payment timing to End of period (most loans and deposits) or Beginning of period (payments happen first, like rent).
Fill in the money fields you are not solving for: PV, PMT, and FV. Use this balance convention: positive PV is the starting savings balance or loan amount. Positive PMT adds to the balance; negative PMT reduces it. FV is the ending savings or outstanding loan balance.
Enter Number of periods N using the same period as your payments (example: 60 if you are counting 60 monthly payment periods).
Enter Interest rate (percent per year). Do not leave it blank if the calculator needs it.
Open Advanced options and set Payments per year (P/Y) and Compounds per year (C/Y) so the rate conversion matches your situation (monthly payments usually means P/Y = 12).
In Advanced options, choose Interest rate type (Nominal APR vs Effective annual rate) so the calculator converts the annual rate correctly.
Click Calculate, then review the solved value, the per-period rate used, totals, and the schedule rows to spot mistakes.

Definitions

Finance: The science of how money is used, managed, and invested. [2]

Present value (PV): Money at time 0 (today).

Future value (FV): Money at the end of the last period (money later).

Payment (PMT): The same repeated amount each period (like a monthly deposit or loan payment).

Number of periods (N): How many payment periods are in the problem (example: 60 months).

Interest rate (annual): A percent per year; it must be converted to a per-period rate that matches your periods.

Payments per year (P/Y): How many payments happen in one year (monthly = 12).

Compounds per year (C/Y): How many times interest is added in one year (monthly compounding = 12).

Nominal APR: A quoted annual rate that does not include compounding effects until you convert it.

Effective annual rate: The true one-year growth rate after compounding is included.

Payment timing: End of period (ordinary annuity) vs beginning of period (annuity due).

Sign (balance convention): PV and FV are starting and ending balances. Positive PMT adds to the balance; negative PMT subtracts from it. This differs from a signed cash-flow equation whose incoming and outgoing flows sum to zero.

Methodology

What this calculator solves

This is a time value of money (TVM) solver. It finds exactly one unknown among PV, FV, PMT, interest rate, or N, using the other inputs you provide. It also converts the annual rate to the per-payment-period rate so it matches your N.

Step 1: Convert the annual rate to the per-payment-period rate

First convert percent to decimal (example: 6% becomes 0.06). Then compute the effective interest rate per payment period (the period used by N):

If Interest rate type is Nominal APR (convert using C/Y): i_comp = (APR_decimal) / (compounds per year). Then i_per_payment = (1 + i_comp)^(C/Y divided by P/Y) - 1.
If Interest rate type is Effective annual rate: i_per_payment = (1 + EAR_decimal)^(1 divided by P/Y) - 1.

Validation: P/Y and C/Y must be whole numbers greater than 0. For real-number math, the calculator requires (1 + i_comp) to be greater than 0.

Step 2: Apply payment timing (end vs beginning)

If payments happen at the end of the period, use the ordinary annuity form. If payments happen at the beginning of the period, each payment gets one extra period of interest, so the payment term is multiplied by (1 + i) compared to end-of-period.

Step 3: TVM equations used

Let i be the interest rate per payment period, and N be the number of periods.

Future value: FV = PV*(1+i)^N + PMT*(((1+i)^N - 1)/i)*due, where due = 1 for end-of-period payments and due = (1+i) for beginning-of-period payments.
Present value: PV = (FV/(1+i)^N) - PMT*((1 - (1+i)^(-N))/i)*due (same due definition).
Payment: PMT = (FV - PV*(1+i)^N) / ( ((1+i)^N - 1)/i * due ).
Zero-rate case: If i is extremely close to 0, use FV = PV + PMT*N, PV = FV - PMT*N, and PMT = (FV - PV)/N to avoid division by zero.
Solve for N: If PMT is not 0, N = ln((FV + PMT*due/i)/(PV + PMT*due/i)) / ln(1+i). If PMT is 0, N = ln(FV/PV) / ln(1+i). This log step follows standard algebra rules for exponent equations. [1]
Solve for interest rate: There is no simple closed form in the general annuity case, so the calculator finds i numerically using a bracketing search and bisection until the TVM equation error is very small.

Schedule and totals

The schedule is built period-by-period using the per-period rate i and your PMT sign. For end-of-period timing: interest_t = balance_{t-1}*i and balance_t = balance_{t-1} + interest_t + PMT. For beginning-of-period timing: apply PMT first, then compute interest on the new balance. The table shows the first requested rows; totals are computed from the same math, and can differ by a few cents depending on whether you round each period.

Common input mistakes this page helps prevent

Rate-period mismatch: N is counted in payment periods, so the calculator converts the annual input into a per-payment-period rate using P/Y and C/Y.
Wrong signs: If a loan has PV positive and PMT also positive, the balance will usually grow instead of shrink. The calculator does not auto-flip signs; it asks you to fix them so your inputs match the real cash flows.
No real solution: Some combinations (especially when solving for N or interest) do not have a real-number answer. In those cases, the solved value shows N/A with a clear reason (for example, log inputs not positive or no bracket found for the rate).