TVM Calculator (Time Value of Money Solver)
Solve any time value of money problem like a financial calculator: find the future value, present value, payment, number of periods or interest rate from the other four, with payments at the start or end of each period.
How it works
FV = PV × (1 + i)ⁿ + PMT × [(1 + i)ⁿ − 1] ÷ i × (1 + i × t) · i = annual rate ÷ periods per year, n = years × periods per year, t = 1 if payments are at the beginning of each period (annuity due), 0 if at the end · N = ln[(FV + k) ÷ (PV + k)] ÷ ln(1 + i) with k = PMT × (1 + i × t) ÷ i · I/Y is found numerically
The time value of money (TVM) equation links five quantities — present value, payment, future value, interest rate and number of periods — so that knowing any four fixes the fifth. It is the same equation built into financial calculators such as the HP 12C and TI BA II Plus and into the spreadsheet functions FV, PV, PMT, NPER and RATE. This solver uses a saver’s convention: the starting amount and the payments go in, the future value comes out, and the rate is a nominal annual rate compounded once per payment period.
Worked example
Saving 200 at the end of every month on top of a 10,000 starting balance at 6% a year (0.5% a month) for 10 years (120 periods): FV = 10,000 × 1.005¹²⁰ + 200 × (1.005¹²⁰ − 1) ÷ 0.005 = 18,193.97 + 32,775.87 = 50,969.84. You deposit 34,000 in total, so 16,969.84 is interest, and the effective annual rate is 6.17%.
Sources: Corporate Finance Institute — Time value of money · Microsoft Support — FV function
Frequently asked questions
What does TVM stand for?
Time value of money: the idea that money available today is worth more than the same amount later because it can earn interest. Every TVM problem uses the same five variables — N, I/Y, PV, PMT and FV.
What is the difference between an ordinary annuity and an annuity due?
In an ordinary annuity each payment is made at the end of the period; in an annuity due it is made at the beginning, so every payment earns one extra period of interest and the future value is (1 + i) times larger.
Why does my financial calculator show negative numbers?
Financial calculators use a cash-flow sign convention: money you pay out is negative and money you receive is positive. This calculator treats the starting amount and deposits as positive inputs and the future value as the positive amount you end up with.
How do I solve for the interest rate?
Choose “Interest rate (I/Y)”, enter the starting amount, the payment, the target future value and the time. There is no closed formula for the rate, so the calculator searches for the rate that makes the equation balance, just as the RATE function does.
Can I use it for a loan?
For a loan, think of the future value as zero and the present value as the amount borrowed — a dedicated loan or amortization calculator is easier for that. This solver is set up for savings and investments that grow toward a target.
Related calculators
Educational estimate, not financial advice. Real contracts, fees, taxes, day-count and rounding rules differ — check the official cost disclosure and your agreement before deciding.