TVM Solver — Time Value of Money
Solve for any of the five TVM variables: periods, interest rate, present value, payment, or future value.
Enter four known values to solve the fifth.
Time Value of Money (TVM) Solver
The time value of money is the principle that a dollar today is worth more than a dollar in the future. The five TVM variables describe every basic financial transaction:
| Variable | Meaning |
|---|---|
| N | Number of periods (years, months, etc.) |
| I/Y | Interest rate per period (%) |
| PV | Present value — value today |
| PMT | Payment per period (annuity) |
| FV | Future value — value at end of N periods |
The TVM equation:
PV × (1+r)^N + PMT × ((1+r)^N − 1) / r + FV = 0
Where r = I/Y per period (as a decimal). For r = 0: PV + PMT × N + FV = 0
Sign convention:
Cash outflows (payments you make) are negative. Cash inflows (amounts you receive) are positive.
Example — saving for a goal:
- PV = −5,000 (you invest $5,000 today)
- PMT = −200 (you add $200/month)
- FV = 20,000 (your goal)
- Solve for N or I/Y
How to use this calculator:
- Select which variable to solve for
- Enter the other four values
- Leave “Periods per year” at 1 for annual, set to 12 for monthly, etc.
Common use cases:
- How long to reach a savings goal (solve for N)
- What interest rate you need to retire on time (solve for I/Y)
- How much a loan is worth today (solve for PV)
- What monthly payment is required (solve for PMT)
- What your investment will grow to (solve for FV)
Periods per year:
If payments are monthly, set periods per year = 12 and enter the annual interest rate. The calculator converts the rate to a per-period rate automatically.