Time Value of Money Calculator
A full TVM solver: enter any four of N, I/Y, PV, PMT and FV and it solves the fifth, just like a BA II Plus. It handles payments at the start or end of each period and different payment and compounding frequencies. Simple future value and present value calculators are below.
Time value of money calculator (TVM solver)
Works like a BA II Plus or HP 12C: enter four of the five values and solve for the fifth. Money you pay out is negative, money you receive is positive.
Future value calculator
Present value of a future amount
The time value of money equation
Every TVM problem solves one equation: PV × (1 + i)N + PMT × (1 + i × type) × ((1 + i)N − 1) ÷ i + FV = 0, where i is the rate per period and type is 1 for payments at the start of each period and 0 for the end. When compounding (C/Y) differs from payments (P/Y), the calculator converts the annual rate to the matching rate per payment: (1 + I/Y ÷ C/Y)C/Y ÷ P/Y − 1.
Example: invest $10,000 (PV = −10,000) and add $200 a month (PMT = −200) at 6% for 10 years (N = 120, P/Y = C/Y = 12). FV = $50,969.84. Change "Solve for" to I/Y and enter that FV and the calculator returns 6%, which shows the equation balances.
| Key | Meaning |
|---|---|
| N | Total number of payment periods (years × P/Y) |
| I/Y | Annual interest rate in percent |
| PV | Value today (a loan you receive is +, an investment you make is −) |
| PMT | Payment each period |
| FV | Value at the end (a balloon or a savings target) |
Common questions
What is the time value of money?
The idea that a dollar today is worth more than a dollar later, because today's dollar can earn interest. TVM math converts money between dates using an interest rate.
How do I calculate future value?
FV = PV × (1 + i)^N for one amount, plus the annuity part for regular deposits. $10,000 plus $200 a month at 6% for 10 years grows to $50,970.
Why is my TVM answer negative?
TVM uses cash-flow signs. If you put money in (negative PV and PMT), the future value you get back is positive. Mixing signs wrongly gives no solution for N or I/Y.
What is the difference between P/Y and C/Y?
P/Y is how many payments you make a year; C/Y is how many times interest compounds a year. For most loans both are 12.
How do I find the interest rate on an investment?
Enter N, PV, PMT and FV and solve for I/Y. The calculator searches for the rate that makes the TVM equation balance.
Sources
Related
General information, not financial, tax or legal advice. Check important numbers with the official source before acting on them.