Time Value of Money Explained Part II
Future Value of Money – High Rolling on the Penny Slots
Say that I received $100,000 from hitting the jackpot on the nickel slots (that’s about as high of a roller as I get). As I’m getting ready to cash out my $100,000 at the casino, they tell me that I could either take the $100,000 now or I could get $106,000 in one year. As you read in the last post, having a dollar now is always better than a dollar in the future since I could invest it. This example adds a little bit of twist now though since we could either take the $100,000 now or wait one year and get $6000 more. So, how do we figure out what to choose? One way is to use the concept of the future value of money.
As in the lemonade stand example, we can calculate what the $100,000 would be worth if we invested it for a year and collected the interest. Let’s say that we’re able to get 5% interest in our savings account. The amount of interest that we would get after investing the $100,000 in one year would be:
$100,000 x 5% = $100,000 x 0.05 = $5000
Adding this to the original amount of $100,000, you end up with a total of:
$100,000 + $5000 = $105,000
The other way to calculate this is to multiply the $100,000 by 1 plus the interest rate:
$100,000 x (1 + 5%) = $100,000 x (1 + 0.05) = $100,000 x (1.05) = $105,000
So if I’m able to invest the $100,000 at 5%, I’ll end up with $105,000 in a year. In finance terms, that means that the future value of $100,000 in 1 year at a 5% interest rate is $105,000. For this case, it makes sense to take the $106,000 that the casino offered to give us in a year since we could only make $5000 in interest compared to the $6000 extra they were offering us to wait a year.
Essentially when you’re calculating future value of money, you’re taking the amount that you have today and calculating what it would be worth in the future if you invested it at a certain interest rate. We’ll do a couple of more examples to help explain this concept. At this point, we’ll stick to terms that are one year long but in future lessons we’ll cover calculating the future values of different time periods.
A Few More Examples of the Future Value of Money – Small Business Financial Mangement
Take the example where you find a $100 bill laying on the sidewalk. If you could get 2% interest in your savings account, what is the future value of the $100 in one year?
For this example, we take the amount that we found and want to calculate what the future value of the money is in one year. The first step is to calculate out the interest that we would get by investing the $100 at 2% for a year:
$100 x 2% = $100 x 0.02 = $2
Since we know the interest is $2, we can add back the $100 that we originally put in the savings account to get a total of:
$100 + $2 = $102
By adding the total interest that we were able to get by investing the $100 in a savings account at 2% to the $100, we were able to calculate the future value of $100 in one year was $102. We can get the same answers by using the shortcut method of multiplying the $100 by 1 plus the interest rate:
$100 x (1 + 2%) = $100 x (1.02) = $102
How Much Interest Is There In The Future Value of Money?
To show how the interest rate affects the future value, let’s modify the previous example. Say you find the $100 but you have a great savings account that gives you 6% per year for investing your money. What is the future value of the $100 after one year?
As in the last example, we need to calculate the interest that we make off of the $100 while it’s in the savings account for one year:
$100 x 6% = $100 x 0.06 = $6
Adding the interest back to the original $100 we invested:
$100 + $6 = $106
Using the other method, we also get the same answer:
$100 x (1 + 6%) = $100 x (1.06) = $106
So in this case, the future value of $100 in one year when you’re able to get 6% interest is $106. Compare this to the $102 future value of the $100 bill when the interest rate that you were able to get was only 2%. As can be seen, the interest rate that we are able to get changes how much money invested today is worth in the future.
Key Takeaways: To find the future value of money, we calculate is how much the money we have today would be worth in the future if we invested at a certain interest rate. In the next lesson, we’ll cover what the present value of money is (essentially the opposite of the future value of money with a few twists).