8/12/2019 Present and Future Value
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Present and Future Value
Suppose you could choose between receiving a new flat screen TV
today, and receiving the sameTV one month from now. Unless you have
unusual preferences, you would choose receiving the
TV today. In general, we prefer present consumption over future
consumption because wediscount the future.How muchwe should
discount the future is determined by the interest rateand the
present value formula. The relationship between present and future
value is oftenreferred to as the time value of money, but it is
important to eep in mind that it is what we dowith the money !e.g.
consumption or investment" that really matters.
#ne of the easiest ways to see this relationship is to imagine
you are putting money into asavings account at your local ban. If
you put $%&& into the account now, you would lie tonow how
much money you will have in one, two and three or more years. This
initial $%&& isreferred to as the principal, and the e'tra
income earned on the principal are interest payments.(e normally
assume there is compound interest, meaning that the interest earned
each period is
applied to the principal and the interest income from all
previous periods. If the ban calculatesand pays compound interest
on an annual basis, we can use the following formula)
t
t rPVFV "%! += , !%"
where *Vtis the future value in t years, +V is the present value
and r is the interest rate !or yield"per annum. In this case the
present value is $%&&. If the annual interest rate is -
then r ise'pressed as a decimal so that the value of the deposit
after one, two and three years will be!rounding to the nearest
cent",
ear #ne) %&$"&.%!%&&$"%!% ==+= rPVFV
ear Two) /.%%&$"&.%!%&&$"%! /// ==+= rPVFV
ear Three) 01.%%,$"&,.%!%&&$"%! 222 ==+= rPVFV .
In general, to find the future value in t periods, multiply the
present value by !% 3 r" to the tpower. #ne can also thin of r as a
growth rate for any variable which grows at a constant rate.
Up to this point, compounding has occurred in discreet periods.
4ontinuous compounding isessentially maing the compounding periods
infinitely small, so that interest is compounding
continuously. In order to calculate future value when using
continuous compounding thefollowing e5uation must be used.
rt
t PVeFV = !/"
