Understand Finance - Finance Tutorials and Finance How To's

This tutorial will give you a great foundation to continue learning about Time Value
of Money. You know that a dollar in your hand today is worth more than a dollar sometime
out in the future. But how much is that dollar worth today? This tutorial will give you
the tools to answer that question.

We’re dealing with present values and future values here. A present value is what
something is worth to us today, whereas a future value is… well, its out in the future!
If we invest $100 today in a savings account earning 3% annually, how much will our $100
be worth in 25 years? Let’s look at this on a timeline and see what is going on here:

"http://www.understandfinance.com/img/1/timeline1.gif" />

We see that at time period 0, our present value, we have our $100. It is a negative
number because it is a cash outflow. That is to say, our wallet is now lighter by
$100 because we have put that money into a savings account. On the right hand side of the
timeline, you see that 25 years later, we want to know the value of our deposit. We’re
solving for our future value! This problem now becomes a simple calculator exercise.
Here’s the steps you take…

Texas Instruments BAII Plus

Step 1. Clear the calculator: Step 2. Annual compounding: Step 3. Set N = 25 Step 4. Set I/Y = 3% Step 5. Set PV = -100 Step 6. Compute FV

Hewlett-Packard 10BII

Step 1. Clear the calculator: Step 2. Annual compounding: Step 3. Set N = 25 Step 4. Set I/YR = 3% Step 5. Set PV = -100 Step 6. Compute FV

If all went well, you saw that your $100 grew to $209.38 after 25
years! Now, try some of the following practice problems on your own. If you are unable to
get the same answers we do, try getting some help in our "http://www.understandfinance.com/forum/">forum.

Practice Problem 1: Calculating Present Values.
Your beautiful newborn baby girl deserves the best. On her 16th birthday, you want to buy
her a brand new car which will cost $35,000 at that time. If you can earn 11.5% annually
on your investments, how much will you need to invest today in order to buy her this
gift?

Solution:
Wow, kids are expensive (see our tutorial on opportunity cost)! We know that N is 16
since we’re buying this car in 16 years. We also know the FV will be $35,000 and our I is
11.5%. Plug this in and solve for PV to get $6,132.96. Maybe this gift
isn’t too expensive afterall!

Practice Problem 2: Calculating the number of compounding
periods.
You just won the lottery and received a check for $450,000! Being someone that
understands the time value of money, you decide to invest it in a mutual fund earning 8%
annually. How many years will it take for your winnings to become $1,000,000?

Solution:
In this one, we are solving for N. Try setting up a timeline and working this one out on
your own. Remember that today we have $450,000 and sometime in the future we want to have
$1,000,000. If you set this up correctly, you should see that it will only take
10.38 years. If you see no solution on your HP10BII or Error
5 on your TI BAII Plus calculator, make sure you put your PV in as a negative number.
Remember, that money is a cash outflow when it goes into the mutual fund!

Practice Problem 3: Finding the Interest Rate
Fifty years ago, your Uncle Tyrell invested $1,000 in a savings account that pays
interest quarterly. During your weekly visit, you spot his bank statement and see that it
is now worth $59,500. What rate of interest has Uncle Tyrell earned over the years?

Solution:
This one is a little tricky. First of all, “quarterly” tells us that we are dealing with
4 payments per year. Make sure your calculator is set up correctly! Now, if we’re dealing
with quarterly payments, what should N be? That’s right–N = 50 years * 4 payments per
year = 200. The rest should be easy enough if you’ve drawn your timeline. You will find
that Uncle Tyrell earned 8.26% on his deposit.