Time Value of Money Explained: How to Calculate TVM

The time value of money (TVM) is a financial concept that states that the present value of an amount of money is worth more than the future value of that same lump sum. This principle comes from the fact there are opportunity costs to consider when comparing the value of receiving money today versus accepting a future payment. The opportunity cost (also called an implicit cost) of a decision is the value of what you will lose or miss out on when choosing one possibility over another.

If you receive money today, you can immediately put it to use. As a simple example, you can park that money in a savings account that offers continuous compounding interest. The value of the money will increase after a number of periods pass and that lump sum accumulates interest. Alternatively, you could invest the money you receive today in an appreciating asset like real estate or purchase stock, both of which have the potential to gain value over time. Due to immediate purchasing power, some investors consider a present-day sum of money to be more valuable than a future sum.

The time value of money formula can be written as:

In this formula, “FV” is the future value of money, “PV” is the present value of money, “i” is an annual interest rate, “n” is the number of compounding periods in a year (assuming compound interest is in play), and “t” is the number of years the money will be invested.

The time value of money formula shows the future value of a present-day sum of money based on the assumption that you will invest that money over a sustained period of time. The time value of money formula is sometimes called the “future value formula” because it helps investors predict how much a specific amount of money will be worth at a set date in the future. The present value formula represents a different money concept: present value as a function of future value. It calculates the value of a future lump sum in present-day dollars.

The present value formula is written as:

In this formula, “PV” equals the present value of money, “FV” equals the future value of money, and “r” is the rate of return. Financial analysts sometimes call this "discounting" future money to arrive at an equivalent value in present-day dollars.

You can use the time value of money formula to determine the future value of an annuity. An annuity is a series of payments that arrive on a regular basis. For instance, if you are a landlord, you receive regular annuities from your tenants via their monthly payments.

A payment made at the end of a recurring period is called an ordinary annuity. A payment made at the beginning of a recurring period is called an annuity due. Annuities that last indefinitely with no end date are called perpetuities.

The formula for calculating the present value of an annuity varies depending on whether you are dealing with ordinary annuities, annuities due, or perpetuities. All of these formulas can be found on a standard financial calculator used in budgeting. The formulas function much like the present value formula for a lump sum of money. They give a present-day valuation for annuities you will receive over the course of a set timeframe in the future.

All investments and investment strategies entail inherent risks and introduce the potential for financial loss or the depreciation of assets. The information presented in this article is for educational, informational, and referential purposes only. Consult a professional investment advisor before making any financial commitments.

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