Time Value of Money

Introduction to Money

A great many of the financial transactions done by ordinary people, you and I, involve paying or receiving money early and receiving or paying money back later. For example, financing the purchase of a home entails receiving money now and paying money back later.

On the other hand, buying mutual fund shares entails the paying out money now and receiving money back later. The same is true, either paying or receiving, about life insurance, bank savings account, invest in real estate, decide to lease rather than buying a car, etc. etc.

All these everyday life deals center on the time value of money. They arise in all fields of business and personal finance planning, real estate, marketing, investments, accounting, insurance, banking, and many other fields.

Some people erroneously believe that a dollar is a dollar is a dollar. The fact is dollars to be paid or received in different time periods have different values. To receive the money, many people would prefer to receive it as soon as they can. On the same token, they would prefer to pay money as late as they can. For most people, that's intuitive.

The Role of Interest - Since a given sum of money due in different time periods does not have the same value, a tool is needed in order to make the different values comparable. That tool is interest, which can be viewed as a way of quantifying the opportunity cost incurred by one who waits to receive money or who give up the opportunity to delay paying it.

For example, if you deposit $1,000 in a savings account and leave it there for one year, you expect to have more than $1,000 in the account at the end of that time. You expect your account to earn interest. You delayed the use of your money and, instead, allowed the bank to use it. You incurred an opportunity cost. The interest the bank gives you is compensation to you for having done so.

Now reverse the situation. Let's say you took out a loan from a bank which will mature in one year, at which time you are obligated to pay $1,000.  However, if you repay the loan today, one year early, you believe you should be required to pay less than the full $1,000. If you forgo the opportunity to delay the repayment, you should be compensated in return by having the amount payable reduced.

Interest Rate - The specific interest rate that should be used to quantify opportunity cost consists of two components: a risk-free rate and a risk premium. At a minimum, the opportunity cost of letting someone else use your money is the rate of return you could have earned by investing it in a perfectly safe instrument.

Here, we have taken up the case of risk-free rate. A reasonable measure of this minimum opportunity cost is the rate of interest available on three-month U.S. Treasury bills which are risk-free.

Simple Interest vs. Compund Interest - There are two ways of computing interest. Simple interest is computed by applying an interest rate to only an original principal sum. Compound interest is computed by applying an interest rate to the total of an original sum and all interest credited to it in earlier time periods.

Future Value of a Single Sum (FVSS) - The most frequently encountered and easiest to understand application of the time-value-of-money concept involves the future value of a single sum. Determination of a future value of a sum of money entails a process of compounding, or increasing, the present value at some interest rate for some period of time.

Basic Time-Value Formula - The most common example is the growth of a sum placed in an interest-bearing savings account. The basic formula for computing the future value of a single sum of money, from which all other time-value formulas are derived, is the following:

FVSS = PVSS (1+i) to the power of n.

Where
FVSS = Future Value of a Single Sum
PVSS = Present Value of a Single Sum
        i = Compound periodic interest rate, expressed as a decimal
       n = Number of periods during which compounding occurs

That is, add the interest rate in decimal to one and raise this sum to a power equal to the number of periods during which the compunding occurs. Then, multiply the result by the present value of the single sum or deposit in question to compute the future value of that sum.

For example, you deposit $5,000 in a new savings account that will earn 9% compound annual interest for nine years.

So, FVSS = 5000 * (1+0.09) to power of 9.
Pick up a calculator and when you solve it, you should get $10,859.47

You will more than double your money if you deposit it for 9 years at 9% compounded interest.

Another safe way to double your money is to fold it over once and put it in your pocket.
- Frank Hubbard