# Time Value of Money

##### Urmi Sengupta| Updated on: March 28, 2023

Money has a variable value. But, this value can change over time. Today's money has a different value than it had in the past or will in the future. We usually understand that because of inflation, money is worth less as time goes on. But, a financial accounting concept that tells you how money's value varies is the time value of money or TVM. It is helpful to determine the value of future cash flows and the impact of financial decisions made on investments that affect the value of money in the future. TVM helps you understand the cost of opportunity lost when you delay in investing the money that you have in hand.  If someone gave you money today or after a few months, the money would be worth more to you today than later.

## What is the time value of money (TVM)?

The time value of money (TVM) states that money is worth more in the present than the same sum of money will be in the future because the money in the present has earning potential in the intervening time period. So, a sum of money now is worth more than it is in the future. So, the present discounted value is the time value of money or TVM. When you delay investing money today, you lose an opportunity to grow the money.

The formula used in accounting to calculate the TVM factors the amount of money, its future value, the time frame considered, and the amount it can earn in that time frame. The number of compounding periods is also considered in calculating the TVM of money in a savings account. This concept also describes why an investor would rather have you give them a sum of money today rather than in the future. This is because an investor knows that the sum of money today has an opportunity to grow in a time when invested.

An example to explain TVM is money that is in a savings account. It earns interest that adds to the principal and then accumulates more interest thanks to the compounding interest principle. So, that money on the day it was invested was worth more than in the future because it had the potential to grow. If the same sum of money were locked in a cupboard or hidden in a box for the same time, it would be worth less because its buying power is reduced due to inflation. So even when the face value of money is the same, it has different values in the present and the future because of the opportunity cost that is lost in any delay in investing that money.

## Formula for the time value of money

The formula for the time value of money can help you precisely calculate the change in the value of money over a specific time. The variables that are used in the formula for TVM are:

FV = Value of money in the future

PV = Present value of money, which is the value of the money that you have now

i = interest rate

n = number of compounding periods per year, which could be daily, weekly, monthly, quarterly, etc.

t = number of years

The formula for TVM is:

FV = PV x [ 1 + (i / n) ] ^ (n x t)

## Time value of money examples

So, if a \$1,000 is invested for one year at 10% interest compounded annually. The value of that money in the future  is:

FV = \$1,000 x [1 + (10% / 1)] ^ (1 x 1) = \$1,100

You can reorder the same formula to find the value of a future sum at today’s value. So, the value that you need today to invest and grow to \$10,000 at 7% interest would be:

PV = \$1,000 / [1 + (7% / 1)] ^ (1 x 1) = \$9,346

## Effect of compounding periods on the future value

As we can see in the formula, the number of compounding periods greatly affects the calculation of the TVM. So, if you take a sum of \$1,000, and apply the formula for different compounding periods of quarterly, monthly, or daily, the future value is:

Quarterly Compounding: FV = \$1,000 x [1 + (10% / 4)] ^ (4 x 1) = \$1,103

Monthly Compounding: FV = \$1,000 x [1 + (10% / 12)] ^ (12 x 1) = \$1,104

Daily Compounding: FV = \$1,000 x [1 + (10% / 365)] ^ (365 x 1) = \$1,105

So, TVM is dependent on the interest rate, time, and the number of times the compounding calculations are computed in a year.

## How does the time value of money relate to opportunity cost?

Money in hand must be invested for it to grow. If it is merely kept as cash, you lose the opportunities to invest it and make positive returns. This is called opportunity cost, an essential factor in the time value of money concept. So, even if you expect to be paid some money in the future, it will be worth less than it would be if you were paid the same sum today.

## Importance of time value of money

When you make investments, you should also consider that the time value of money can help guide investment decisions. If there is a choice of similar projects, but one returns \$10,000 in a year and the other returns the exact same amount after three years, an investor would not consider the returns equal. The payout after a year is higher than the one after three years because it has more present value.

## How is the time value of money used in finance?

The time value of money is used in most decisions in finance. It is the central concept in the discounted cash flow (DCF) analysis, a method for valuing investment opportunities. Financial planning and risk management also use the TVM to make better financial decisions. It can be helpful in

Investors and financial firms use TVM to evaluate and choose between different investment choices. Lenders find TVM useful to fix interest rates and loan tenures. It can also be used in the pricing of products and fixing wages.       