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Finance

 presentvalue
 present value of an amount

 Calling Sequence presentvalue(amount, rate, nperiods)

Parameters

 amount - given amount rate - interest rate nperiods - number of periods

Description

 • The function presentvalue gives the value at period=0 of an amount given at period=nperiods. The interest rate is given by rate.
 • The present value concept is arguably the most important concept behind the personal finance portion of the Finance package. It allows one to properly account for the time value of money.
 • presentvalue is the appropriate function to calculate the present value of a pure discount bond (zero-level bond).
 • Since presentvalue used to be part of the (now deprecated) finance package, for compatibility with older worksheets, this command can also be called using finance[presentvalue]. However, it is recommended that you use the superseding package name, Finance, instead: Finance[presentvalue].

Examples

I will require 100 units in three years. I will receive 12% per year at the bank. How much should I deposit now so that I obtain the appropriate amount in 3 years?

 > $\mathrm{with}\left(\mathrm{Finance}\right):$
 > $\mathrm{presentvalue}\left(100,0.12,3\right)$
 ${71.17802478}$ (1)

This can be calculated as:

 > $\frac{100}{{\left(1+0.12\right)}^{3}}$
 ${71.17802478}$ (2)

Now suppose that the interest is compounded monthly. The calculation proceeds as follows:

 > $r≔\mathrm{effectiverate}\left(0.12,12\right)$
 ${r}{≔}{0.126825030}$ (3)
 > $\mathrm{presentvalue}\left(100,r,3\right)$
 ${69.89249499}$ (4)

The effect of the compounding over shorter periods is easily seen.

I have been offered a zero-level bond paying 1000 units in 5 years for 800 units. The risk of default is nil. Should I buy the bond if the interest rate is 10%?

 > $\mathrm{presentvalue}\left(1000,0.10,5\right)$
 ${620.9213231}$ (5)

Answer: it is definitely not a good deal. The bond would be yielding

 > $\mathrm{fsolve}\left(\mathrm{presentvalue}\left(1000,\mathrm{rate},5\right)-800,\mathrm{rate}\right)$
 ${0.04563955259}$ (6)