A time value of money solver laid out like the five TVM keys on a BA II Plus. Enter any four of N, I/Y, PV, PMT and FV, set payments per year and BGN or END mode, then press Solve on the one you want. The AMORT section splits any range of payments into principal and interest.
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Try an example:
Payments at
Sign convention: money you receive is positive, money you pay out is negative (a loan you take is +PV, your payments are −PMT). Press Solve next to the value you want.
Result–
Show the formula with your numbers
Amortization (AMORT)
Schedule view
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How to use the Financial Calculator (TVM)
Set P/Y and C/Y: payments per year (12 for monthly) and compounding per year, usually the same.
Choose END or BGN: END for loans and most savings plans, BGN when payments are made at the start of each period, like rent or leases.
Enter four of the five values using the sign convention: money you receive is positive, money you pay is negative.
Press Solve next to the unknown value. The answer, rate per period, total interest and the formula appear on the right.
Check the amortization: enter P1 and P2 and press Calculate AMORT, or browse the full schedule and download it as CSV.
The time value of money equation
Every TVM problem is one equation with five variables. With i the interest rate per payment period and k = 1 in BGN mode or 0 in END mode:
The equation is set to zero because the cash you receive and the cash you pay must balance once interest is counted. That is why the sign convention matters: on a loan the bank gives you the PV (+) and you pay it back through PMT (−). The rate per period comes from the annual rate: i = (1 + I/Y ÷ 100 ÷ C/Y)C/Y ÷ P/Y − 1, which reduces to I/Y ÷ 100 ÷ P/Y when payments and compounding have the same frequency.
Worked examples
Problem
Inputs (P/Y = 12 unless noted, END)
Solve
Answer
30-year mortgage payment
N 360, I/Y 6.5, PV 300,000, FV 0
PMT
−1,896.20 a month; total interest about $382,633
Retirement savings
N 360, I/Y 7, PV −10,000, PMT −500
FV
691,150.47
How much can I borrow
N 60, I/Y 7.5, PMT −450, FV 0
PV
22,457.39
Return on an investment
P/Y 1: N 10, PV −10,000, PMT 0, FV 20,000
I/Y
7.1773% a year
Months to pay off a card
I/Y 22, PV 5,000, PMT −200, FV 0
N
33.75 (34 payments, the last one smaller)
Annuity due vs ordinary
P/Y 1: N 10, I/Y 5, PV 0, PMT −1,000
FV
END 12,577.89, BGN 13,206.79
Tips for getting the right answer
Match N, P/Y and PMT. If payments are monthly, N counts months and PMT is the monthly amount. A common mistake is entering N = 30 for a 30-year monthly loan.
Enter I/Y as a percentage, not a decimal: 6.5 means 6.5% a year.
Use FV for balloon payments. A loan with a $50,000 balance due at the end has FV = −50,000.
Nominal vs effective rate. I/Y is the nominal annual rate. The result panel also shows the effective annual rate: 12% compounded monthly is 12.6825% effective.
Clear old values. Like the CLR TVM key, the Clear button empties all five fields so a leftover FV or PMT doesn't skew the next problem.
Frequently asked questions
How do I solve a mortgage payment with this financial calculator?
Set P/Y to 12 and END mode, then enter N = 360 (30 years × 12), I/Y = 6.5, PV = 300000 and FV = 0, and press Solve next to PMT. The answer is −1,896.20: a monthly payment of $1,896.20, shown as negative because it is money you pay out.
Why do I get an error when solving for I/Y or N?
The cash flows need opposite signs. If PV, PMT and FV are all positive (or all negative), no interest rate can balance them. For a loan, enter the amount borrowed as a positive PV and the payment as a negative PMT; for an investment, enter the deposit as a negative PV and the payout as a positive FV.
What is the difference between BGN and END mode?
END (an ordinary annuity) assumes each payment is made at the end of the period, which is how most loans work. BGN (an annuity due) assumes payments at the start of each period, so every payment earns one extra period of interest. For example, $1,000 a year for 10 years at 5% grows to $12,577.89 in END mode and $13,206.79 in BGN mode.
What do P/Y and C/Y mean?
P/Y is the number of payments per year and C/Y is the number of times interest compounds per year. They are usually equal. When they differ, for example monthly payments on a Canadian-style mortgage compounded semiannually, the calculator converts I/Y into the correct rate per payment period with i = (1 + I/Y ÷ C/Y)^(C/Y ÷ P/Y) − 1.
Is N the number of years?
No. N is the total number of payments, so a 30-year monthly loan has N = 360. Use the "Set N = years × P/Y" button to convert years automatically, like the 2nd xP/Y key on a BA II Plus.
What formula does the TVM solver use?
It solves PV(1+i)^N + PMT(1+i·k)((1+i)^N − 1)/i + FV = 0, where i is the rate per payment period and k is 1 in BGN mode and 0 in END mode. PV, PMT, FV and N have closed-form solutions; I/Y is found numerically by bisection.
Does the amortization schedule match a BA II Plus?
Yes, it uses the same logic: interest each period is the balance times the periodic rate, principal is the payment minus interest, and signs follow the calculator's convention. The calculator does not round interest to cents each period, so very long schedules can differ from a lender's statement by a few cents.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.