TVM Solver - Time Value of Money

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.

This is the full five-variable solver, the one that behaves like the TVM keys on a financial calculator: give it any four and it returns the fifth, with regular payments and a periods-per-year setting.
If all you want is a lump sum grown forward or discounted back, with no payments and annual compounding, the time value of money calculator does the same job in three boxes and returns the same figures to the cent.

The five TVM variables describe every basic financial transaction:

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 put 5,000 in today)
• PMT = −200 (you add 200 a month)
• FV = 20,000 (your goal)
• Solve for N or I/Y

Run that one at 6% a year with 12 periods per year and N comes back as 57.68, so about four years and ten months. Set PMT to 0 and leave the 5,000 to compound on its own and N jumps to 277.95 periods, just over 23 years. The monthly 200 does almost all the work, which is the usual answer whenever the starting balance is small.

How to use this calculator:

1. Select which variable to solve for
2. Enter the other four values
3. 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.