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Unformatted text preview: Time Value of Money (TVM)
Time Value of Money (TVM) What would you rather have? $100 today or $100 in 1 year Why did we choose today? We have the option to invest that $100 into a savings account (or some other investment) and earn interest.
Inflation our purchasing power gets eroded over time Today think about the cost of gasoline. As gas costs go up we do not have as much money to buy other goods or services Well, what is that $100 worth in the Well, what is that $100 worth in the future? This is a complicated question. Several factors need to be considered.
Let’s assume we are going to go a local bank and will open a savings account Simple Interest
Simple Interest We earn interest on the principle
Examples 6% interest rate
$100 x .06 = $6 in interest At the end of year 1 we have our principle and interest $100 + $6 = $106
At the end of year 2
$106 + $6 = $112 12% interest rate
$100 x .12 = $12 in interest $100 + $12 = $112 at the end of year 1
$112 + $12 = $124 at the end of year 2 Compound Interest
Compound Interest We earn interest on the principle; in addition we earn interest on interest
6% interest $100 x .06 = $6 in interest
$100 + $6 = $106 at the end of year 1
Year 2 $106 x .06 = $6.36 in interest $106 + $6.36 = $112.36 at the end of year 2 12% interest $100 x .12 = $12 in interest
$100 + $12 = $112 at the end of year 1
$112 x .12 = $13.44 in interest
$112 + $13.44 =$125.44 at the end of year 2
That is $1.44 more than we would have had compared to simple interest Everything we have done has been based upon annual compounding.
What happens if we compound more often? Do we have to calculate everything by hand?
No. Open your books and turn to the TVM tables. We have been calculating a Future Value
Notice, the formula at the top of the page.
Now look at 12% for 2 periods.
You will see a factor of 1.2544
$100 x 1.254 = $125.44 If someone offered you $100 today or $125.44 two years from now assuming you could earn 12% interest, then which would you choose?
Doesn’t matter they are equal Why should I care about this?
Why should I care about this? Well, in our society people with money (banks typically) are using this
Most you have a credit card. Your credit card is probably compounding daily. Compounding works for us as an investor but against us as a borrower If you bought a car or a house, then your monthly payment was calculated using TVM
One day you are going to retire. Wouldn’t be great to figure out how much money you needed to save ...
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- Spring '08
- Financial Accounting