Solve for any TVM variable - present value, future value, payment, rate, or periods - with annuity due and ordinary annuity modes.
Enter any four of the five standard TVM variables - present value, future value, payment, rate, or periods - and the tool solves for the missing one, in ordinary annuity mode (payments at period end) or annuity due mode (payments at period start). The mistake behind most wrong answers: the rate must match the payment interval, so 6% annual with monthly payments means 0.5% per period, not 6. Toggling annuity due shifts every payment one period earlier, so present and future values scale by a factor of (1 + i). Everything is computed in your browser; the amounts you enter never leave the page.
A concrete input and expected output from the current implementation.
Input
Loan of $200,000 at 6% annual interest, 30-year term, equal monthly payments at the end of each month, future value 0. Solve for the payment.
Expected output
$1,199.10 per month.
The term is 360 monthly periods and the monthly rate is 6% / 12 = 0.5%, so the payment is $200,000 x 0.005 / (1 - 1.005^-360) = $1,199.10 - the standard 30-year mortgage figure of $5.9955 per $1,000 borrowed.
All five inputs obey one equation: FV = PV(1+i)^n + PMT x ((1+i)^n - 1) / i, with the payment term multiplied by (1+i) in annuity due mode. Give any four of the five and the fifth is determined - directly for PV, FV, and PMT, by iteration for the rate, the one variable with no closed-form solution.
The rate and the period count must be expressed in the payment interval: monthly payments need a monthly rate (annual rate divided by 12) and the term in months. Annuity due moves each payment one period earlier, so for identical inputs its present and future values are the ordinary values multiplied by (1+i).
Each payment arrives one period earlier, so the payment needed for the same present or future value divides by (1 + i). At 0.5% per month that is roughly 0.5%: the $1,199.10 payment on a $200,000, 30-year, 6% loan becomes about $1,193.13. The gap scales with the rate, so it matters most on high-rate, short-term contracts.
A balloon fits: enter the balloon amount as the future value alongside the level payment. Payments that vary from period to period cannot be represented in one calculation - the five-variable model assumes a single payment repeated every period. Split the schedule into separate segments, each with its own rate and balance.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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