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## Understanding the Time Value of Money

By JLP | January 3, 2006

Earlier, I showed you how to calculate the present value of an annuity. Today, I hope to show you how to make choices regarding your money by showing you two deals.

DEAL 1:
Someone offers you \$100 today or \$105 a year from now, which one would you choose?

The correct answer is, “It depends.” It depends on what the current interest rate environment is. Let’s say for this example that the only available way for you to utilize the \$100 is in a bank account that pays 5% per year. If that were the case, you could take the \$100 now or \$105 a year from now and it wouldn’t make a difference to you.

DEAL 2:
Someone offers you \$100 today or \$105 a year from now, but you know that you can get 6% interest on your money at another bank. Which one would you choose?

This example can best be explained using this formula:

Present Value = Future Value X [1/(1 + i)N]

We are solving for the present value. We know the future value is \$105. We know the interest rate (i)at the other bank is 6% (.06 as a decimal). N is the number of years, which for this example is 1. X is the multiplication sign. So, the formula looks like this:

Present Value = \$105 X [1/(1 + .06)1]

Present Value = \$105 X [1/(1.06)1]

Present Value = \$105 X [1/1.06]

Present Value = \$105 X .9433962

Present Value = \$99.06

So, based on an interest rate of 6%, \$105 a year from now is only worth \$99.06 today. (If you want to double check the math, multiply 99.06 by 1.06 and see what the answer is. It should be really close to 105.) For this example, you would do better to take the \$100 now and invest it at 6% so that you had \$106 a year from now.