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Solve for the level periodic payment on any time-value-of-money problem — a loan, a lease, a savings goal, or a bond. Supports ordinary annuities and annuity-due (payments at start of period).
The TVM equation is PV·(1+r)ⁿ + PMT·((1+r)ⁿ − 1)/r · (1 + r·type) + FV = 0, with type = 0 for ordinary annuities and 1 for annuity due. Solving for PMT gives the level payment that satisfies both the present-value and future-value constraints simultaneously.
Time Value of Money — the principle that a dollar today is worth more than a dollar tomorrow because it can earn interest. The five variables PV, FV, PMT, N, and rate are linked by one equation and this solver holds four to find the fifth.
Ordinary = payments at the end of each period (most loans). Due = payments at the start (rent, some leases). The payment on an annuity due is slightly lower because each payment sits an extra period.
By sign convention, PV as a positive number means money you're receiving (loan proceeds), so the payment is an outflow shown negative. We display the absolute value for readability.
Yes — same formula, same sign conventions. Set type=0 for ordinary annuity and type=1 for annuity due to reproduce our answer.
Yes. Set PV to your starting balance, FV to your target, rate to your APY, and n to the number of deposit periods. The solver returns the deposit per period needed.
Results are estimates for educational purposes only and are not financial advice. Verify with a qualified professional before making decisions.
Last updated October 2026