Understanding the Time Value of Money (TVM)
The concept of the Time Value of Money (TVM) is a cornerstone of finance. It's the idea that a sum of money is worth more now than the same sum will be at a future date due to its potential earning capacity. Our Finance Calculator is a versatile tool that allows you to solve for any one of the five key TVM variables: Present Value (PV), Future Value (FV), Number of Periods (N), Interest Rate (I/Y), and Periodic Payment (PMT).
The TVM Formulas
This calculator can solve for different variables depending on what you provide. The core formulas it uses are for Present Value and Future Value.
Present Value (PV) Formula
The PV formula calculates the current worth of a future sum of money or stream of cash flows given a specified rate of return.
PV = FV / (1 + r)^nFuture Value (FV) Formula
The FV formula calculates the value of a current asset at a specified date in the future based on an assumed rate of growth.
FV = PV * (1 + r)^nWhere:
- PV = Present Value
- FV = Future Value
- r = Interest Rate per period
- n = Number of periods
- PMT = Periodic Payment (used in more complex annuity formulas which this calculator can also solve for)
Practical Example: Saving for a Goal
Let's say you want to have $20,000 saved up in 5 years for a down payment on a house. You find an investment account that offers an average annual return of 7%. You want to know how much you need to invest today (the Present Value) in a single lump sum to reach that goal.
- Future Value (FV): $20,000
- Number of Periods (N): 5 years
- Interest Rate (I/Y): 7%
- Payment (PMT): $0 (since it's a lump sum investment)
You would use the calculator to solve for Present Value (PV).PV = $20,000 / (1 + 0.07)^5 ≈ $14,259.69
This means you would need to invest approximately $14,260 today to have it grow to $20,000 in five years at a 7% annual return, without making any additional contributions.