*Author: *Lori Alden

*Audience:* High school
and college economics students

*Time required:* About 30
minutes

*NCEE Standards*: **12**,
15

*Summary*: This exercise
demonstrates that ten payments of $100,000 over a ten year period
does not equal $1,000,000. A simple net present value equation
is used.

*Student handout*:

Joe just won $1,000,000 in a
lottery. He plans to build a house, travel and buy lots of
CDs. But when he goes to collect his prize he's told that he
can't have it all at once. Instead, the lottery officials
say they'll pay him $100,000 today, plus $100,000 a year for the
next 9 years. That's okay, Joe thinks, $100,000 times 10
payments is still $1,000,000. Or is it?

Not even close. Since dollars
received in the future aren't worth as much as dollars received
today, Joe's prize is worth much less than $1,000,000. To
see how much Joe really won, you need to ask this question:
How much money would Joe need to put in the bank today to be able
to collect $100,000 a year over a 10-year period?

The answer depends on the rate of
interest Joe can get on his savings. If the interest rate is
7%, then Joe could withdraw $100,000 from his account one year
from now by putting only $93,458 in the bank today. We
call this amount the present value of $100,000 received next year,
assuming the interest rate is 7%.

Here's a simple formula for
calculating the present value (PV) of any future value (FV)
received t years from now, assuming that the interest rate is r.

PV = FV/(1 + r)^{t}

For example, the present value of a
$100,000 payment that would be received two years from now equals:

PV = $100,000/(1.07)^{2}

= $87,344

To find out to find out the present
value of Joe's lottery winnings before taxes, have your students calculate
the rest of the values in the first column, then sum the
total.

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