### Money Math

While I’m on financial topics, if you don’t know how to do “time value of
money”
math you should stop and learn about it right now. For all
I know I’m the only person who didn’t learn this in high school, but
in case there’s someone else, here’s a blog post.

Because of inflation and ability to earn interest, a dollar today is
not the same as a dollar next year. To compare two financial choices
(say, renting a house vs. buying a house), you need to convert the
choices to money at the same point in time, just as comparing two
measurements requires them to be in the same units.

The buttons that make a calculator a financial calculator are the ones
that let you convert any series of cash flows (money spent or earned)
to the value of that series at a point in time.

The calculator buttons are:

• n – number of periods of time
• i – interest rate per period of time
• PMT – a regular per-period cash flow
• PV – present value, i.e. value of all PMT and FV at time 0
assuming rate i
• FV – future value, i.e. value of PV and all PMT at time n assuming
rate i

A financial calculator can solve for any of these given the other
four.

In a spreadsheet, there’s a separate function depending on what you
want to solve for. From the OpenOffice docs:

• PV(Rate; NPER; PMT; FV; Type)
• FV(Rate; NPER; PMT; PV; Type)
• RATE(NPER;PMT;PV;FV;Type;GUESS)
• NPER(Rate;PMT;PV;FV;Type)
• PMT(Rate; NPER; PV; FV; Type)

The “type” is 0 if PMT comes at the end of the periods, and 1 if it
comes at the beginning.

Next time you have a financial decision, try to break it down into
cash flows and you may find you can get a handle on it with these
formulas.

Caveats:

• The calculations are sensitive to the interest rate you pick. If you start
picking overoptimistic rates you will make all kinds of bad decisions.
• In addition to only comparing money amounts at the same point in time,
you can only compare money amounts if they are both in real dollars or
both in nominal dollars. That is, be sure to reduce your interest
rates to consider inflation when appropriate.
• These formulas assume a steady rate, which is very misleading for
stocks and other risky assets. Actual results will be in a wide
range. When planning retirement savings, you need to run the numbers
with a very pessimistic rate of return, not only with an average one. You
can also find software that uses monte carlo
simulation
to show a spread of possible returns.

(This post was originally found at http://log.ometer.com/2007-08.html#26)