Máy tính tài chính
The detailed guide below is currently available in English.
The four building blocks of time value
Every TVM problem connects four quantities: a present value (PV), a payment per period (PMT), an interest rate per period (r), and a number of periods (n). Given any three, the fourth follows:
- FV = PV(1+r)n + PMT·((1+r)n − 1)/r
- PV = (FV − PMT·((1+r)n − 1)/r) / (1+r)n
- PMT = (FV − PV(1+r)n)·r / ((1+r)n − 1)
- N = ln((FV·r + PMT)/(PV·r + PMT)) / ln(1+r)
When r is zero the formulas collapse to simple sums: FV = PV + PMT·n, and so on.
Sign convention used here
Enter every amount as a positive number: PV is a lump sum you start with (or owe), and PMT is a contribution made at the end of each period. The calculator applies the standard equations internally and reports results from your perspective, so a payment tab that aims at a goal returns the positive contribution required.
Remember to match units: a monthly rate needs the number of monthly periods, an annual rate needs years. Dividing an annual rate by 12 is a reasonable approximation for monthly periods.
Câu hỏi thường gặp
What counts as one "period"?
Whatever you want — a month, quarter, or year. The rate and the number of periods just have to use the same unit: 6% per year over 30 years, or 0.5% per month over 360 months, describe the same loan.
How is this different from the loan calculator?
They share the same math. The loan calculator formats the answer as a payment schedule; this one solves any of the four variables, so it also handles savings goals and growth questions.
Why does the payment result assume end-of-period payments?
That is the ordinary annuity convention, and it matches how most loans and many savings plans work. Payments at the beginning of each period (annuity due) would be worth slightly more; multiply by (1+r) to convert.