Financial Calculator (TVM Solver)
This financial calculator solves the time-value-of-money equation for any one of its five values: number of periods (N), annual interest rate (I/Y), present value (PV), payment (PMT) or future value (FV). Example: 10,000 invested today plus 100 a month for 120 months at 6% grows to a future value of 34,581.90.
How it is calculated
A financial calculator links five values: the number of periods N, the interest rate I/Y, the present value PV, the regular payment PMT and the future value FV. Know any four and the fifth is fixed. That one relationship covers savings plans, loans, leases and retirement withdrawals – they differ only in which value is unknown and in the signs.
The equation
PV · (1 + i)^N + PMT · ((1 + i)^N − 1) ÷ i + FV = 0, where i is the interest rate per period (annual rate divided by the payments per year). If payments are due at the beginning of each period, the payment term is multiplied by (1 + i). At 0% interest it simplifies to PV + PMT · N + FV = 0.
Signs: the one rule to remember
Money leaving your pocket is negative, money coming in is positive. For a savings plan you enter the deposit and the payments as negative numbers and get a positive future value. For a loan the amount you receive (PV) is positive and the payments come out negative. If all amounts have the same sign there is no solution – nobody pays in and pays out at the end as well.
Worked example: savings
PV = −10,000, PMT = −100, N = 120 months, I/Y = 6%, monthly payments at the end of each month. Rate per period: 6% ÷ 12 = 0.5%. PV · (1 + i)^N = −18,193.97; payment term = −16,387.93; so FV = 34,581.90. You paid in 22,000 in total, and 12,581.90 is interest. With payments at the beginning of each month the future value is 34,663.84.
More examples
- Loan payment (solve for PMT): PV = 200,000, N = 360, I/Y = 6%, FV = 0 gives PMT = −1,199.10 a month; the interest over the whole term is 231,676.38.
- Interest rate (solve for I/Y): 1,000 becoming 2,000 in 10 years with yearly compounding requires 7.1773% a year.
- Time (solve for N): at 6% a year, 1,000 doubles after 11.90 years.
- Capital needed (solve for PV): to withdraw 1,000 a month for 240 months at 4%, you need 165,021.86 today (shown as a negative PV, because you pay it in).
Solving for the interest rate has no closed formula; the calculator searches numerically and reports when no rate fits the values.
Frequently asked questions
What do N, I/Y, PV, PMT and FV mean?
N is the number of payment periods, I/Y the nominal interest rate per year, PV the present value (the amount at the start), PMT the regular payment per period and FV the future value (the amount at the end). These are the five keys of the time-value-of-money row on a financial calculator.
Why is my result negative?
Because of the sign convention: amounts you pay are negative and amounts you receive are positive. A loan of 200,000 (positive PV) gives a negative payment of −1,199.10 – money leaving your account every month.
Why does the calculator say there is no solution?
Usually the signs are the cause: if PV, PMT and FV all have the same sign, no interest rate or term can balance them. For a loan it also happens when the payment is smaller than the interest of the first period, so the debt would never shrink.
What is the difference between END and BGN?
END means payments at the end of each period (typical for loans), BGN at the beginning (typical for rent, leases and many savings plans). Each payment earns interest for one more period in BGN mode: 34,663.84 instead of 34,581.90 in the savings example.
How is the interest rate per period calculated?
The annual rate is divided by the number of payments per year: 6% with monthly payments is 0.5% per month. Interest is compounded once per payment period, which is the standard setting on financial calculators.
Sources and legal basis
- Hewlett-Packard: hp 12c financial calculator – user’s guide, Appendix D “Formulas Used” (compound interest equation with PV, PMT, FV, n, i and payment mode Begin/End; sign convention for cash flows)
- OpenStax: Principles of Finance, Chapter 8.2 “Annuities” (present and future value of level payments, ordinary annuity and annuity due)
As of: · Editorial policy
Related tools
- Present Value CalculatorPresent value calculator: what is a future amount or a stream of payments worth today? Handles lump sums, annuities and perpetuities, with a rate comparison.
- Future value calculatorFuture value calculator: final value from a starting amount, interest and regular deposits – or the present value of a future sum. With formula and table.
- Annuity CalculatorAnnuity calculator: enter a principal or payment, the interest rate and the term to get the payment, present value or future value – ordinary or annuity due.
- Compound interest calculatorCompound interest calculator with monthly contributions: final balance, interest earned, inflation-adjusted value, time to reach a goal, chart and yearly table.
- Amortization CalculatorAmortization calculator: enter loan amount, interest rate and term to get the monthly payment and a full schedule of interest, principal and balance.
- Interest rate from payment calculatorCalculate the interest rate from a loan payment: nominal and effective annual rate from loan amount, monthly payment and term – also with a balloon payment.
- Mortgage calculatorMortgage calculator: monthly payment with taxes, insurance, PMI and HOA from home price, down payment and rate – extra payments, 15 vs 30 years, amortization.
- HELOC CalculatorHELOC calculator: enter home value, mortgage balance and the lender’s CLTV limit to get your available credit line and the payments in draw and repayment.
- Student loan calculatorStudent loan calculator: monthly payment, interest that builds up during the grace period and total cost over any repayment term, with 2026-27 federal rates.