Time Value of Money

The time value of money (TVM) is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also sometimes referred to as present discounted value.

The time value of money draws from the idea that rational investors prefer to receive money today rather than the same amount of money in the future because of money’s potential to grow in value over a given period of time. For example, money deposited into a savings account earns a certain interest rate, and is therefore said to be compounding in value.

Basic Time Value of Money Formula

Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:

• FV = Future value of money
• PV = Present value of money
• i = interest rate
• n = number of compounding periods per year
• t = number of years

Based on these variables, the formula for TVM is:

FV = PV x [1 + (i / n)] ^{(n x t)}

There are five (5) variables that you need to know

1. Present value (PV)– This is your current starting amount.  It is the money you have in your hand at the present time, your initial investment for your future. 
2. Future value (FV)– This is your ending amount at a point in time in the future. It should be worth more than the present value, provided it is earning interest and growing over time.
3. The number of periods (N)– This is the timeline for your investment (or debts). It is usually measured in years, but it could be any scale of time such as quarterly, monthly, or even daily.
4. Interest rate (I)– This is the growth rate of your money over the lifetime of the investment. It is stated in a percentage value, such as 8% or .08.
5. Payment amount (PMT)– These are a series of equal, evenly-spaced cash flows.