What are the five TVM variables?

N is the total number of compounding periods. I/Y is the annual interest rate as a percent. PV is the present value (lump sum at time zero). PMT is the recurring payment per period. FV is the future value (lump sum at the end of N periods).

How does the sign convention work?

Cash you receive is positive; cash you pay out is negative. When borrowing, PV is positive and PMT and FV are negative. When saving, PV and PMT are negative and FV is positive. Mixing signs incorrectly is the most common source of wrong answers.

What does P/Y control?

P/Y is payments per year. Use 12 for monthly, 4 for quarterly, 52 for weekly, 26 for biweekly, 1 for annual. The calculator converts the annual I/Y to a periodic rate using this setting.

When should I use BEGIN vs END mode?

END (the default) means payments occur at the end of each period, which is correct for nearly all loans, mortgages, and ordinary savings plans. BEGIN means payments occur at the start of each period (an annuity due), used for some leases and advance-paid rent.

Is the output financial advice?

No. The calculator is a general illustration tool and is not financial, investment, tax, or legal advice. Always consult a qualified professional for real financial decisions.

Financial END

N— I/Y— PV— PMT— FV—

Enter a value, press a TVM key to store. Press a TVM key with no entry to solve for it.

P/Y

Financial Calculator (TVM)

A time-value-of-money solver in the spirit of the HP-12C. Five variables — N, I/Y, PV, PMT, FV — describe nearly any loan, savings plan, lease, or annuity. Enter values for the four you know, then press the key for the unknown to solve for it.

Output is for general illustration only and is not financial, investment, tax, or legal advice. See our Terms.

If you just want to calculate a mortgage payment, try our dedicated Mortgage Calculator with PMI, taxes, and insurance built in.

The five TVM variables

N — total number of compounding periods (e.g., 360 for a 30-year monthly mortgage).
I/Y — annual interest rate, expressed as a percent (e.g., 6 for 6%). The calculator divides this by P/Y internally to get the periodic rate.
PV — present value: the lump sum at time zero (e.g., the loan amount you receive, or the starting balance of a savings account).
PMT — recurring payment per period (e.g., the monthly mortgage payment, or a recurring deposit).
FV — future value: the lump sum at the end of N periods (e.g., the balloon payment, or the savings goal).

Internally, the calculator solves the standard time-value-of-money identity:

PV + (1 + i·t)·PMT·[(1 − (1+i)^(−N)) / i] + FV·(1+i)^(−N) = 0

where i is the periodic rate (I/Y ÷ 100 ÷ P/Y) and t is 0 for END mode or 1 for BEGIN mode. The four "store" values are substituted in and the equation is solved for the fifth — closed-form for everything except I/Y, which uses Newton's method.

How to use it

Type a value on the display, then press a TVM key (N, I/Y, PV, PMT, FV) to store it. The cell above the display lights up to confirm.
Press a TVM key without entering a value to solve for it. The result appears in the display and the cell highlights in blue.
The five register cells across the top of the display show every stored or solved value, so you can see the full state at a glance.
Press Clear once to clear the current entry. Press it twice for an all-clear that resets every TVM register.
RCL recalls a stored value to the display; STO stores the displayed value into the most-recently-pressed register; ENT pushes the displayed value into the register slot.
Press AMORT after solving to see a cumulative principal/interest summary.

Sign convention (important)

TVM math relies on signed cash flows: cash you receive is positive, cash you pay out is negative. Mixing signs incorrectly is the most common source of wrong answers.

Borrowing money: PV is positive (loan proceeds come in); PMT and FV are negative (you pay them out).
Saving money: PV and PMT are negative (you put money in); FV is positive (you withdraw it later).
If you forget the sign and the answer looks "off by a minus," that's almost always why.

Settings: P/Y and BEGIN / END

P/Y — payments per year. Use 12 for monthly, 4 for quarterly, 52 for weekly, 26 for biweekly, 1 for annual. The calculator converts the annual I/Y to a periodic rate using this setting.
END (default) — payments occur at the end of each period. This is correct for the vast majority of loans, mortgages, and ordinary savings plans.
BEGIN — payments occur at the start of each period (an "annuity due"). This is correct for some leases, advance-paid rent, and certain insurance products.

Worked examples

30-year fixed mortgage — Borrow $300,000 at 6% APR, monthly payments. Set P/Y = 12, N = 360, I/Y = 6, PV = 300000, FV = 0; solve for PMT → about -1798.65 per month.

Long-term savings — Save $500/month for 30 years at 7% APR. Set P/Y = 12, N = 360, I/Y = 7, PV = 0, PMT = -500; solve for FV → about 609,985.

Loan payoff time — Pay $400/month against a $20,000 balance at 9% APR. Set P/Y = 12, I/Y = 9, PV = 20000, PMT = -400, FV = 0; solve for N → about 63 months.

Implied interest rate — A $25,000 car loan repaid as $500/month for 60 months. Set N = 60, PV = 25000, PMT = -500, FV = 0; solve for I/Y → about 7.42%.

The "Example: 30-yr loan" button auto-loads the first example so you can see exactly which registers get populated.

Amortization (AMORT)

After solving for PMT on a loan, press AMORT to see how each period's payment splits between principal and interest. The summary shows total interest paid, total principal repaid, and the remaining balance — useful for tax planning, refinance decisions, and understanding why early loan payments are mostly interest.