Python for Finance

Chapter 3
On the right-hand side of the preceding equation, the first one is the present value
of one future cash flow, while the second part is the present value of annuity. The
variable type takes a value of zero (default value); it is the present value of a normal
annuity, while it is an annuity due if type takes a value of 1. The negative sign is
for the sign convention. If using the same notation as that used for the functions
contained in SciPy and numpy.lib.financial, we have the following formula:
Here are several examples using both Equation (14) and the pv() function from
SciPy. James intends to invest x dollars today for the next 10 years. His annual rate
of return is 5%. During the next 10 years, he will withdraw $5,000 at the beginning of
each year. In addition, he hopes that he will have $7,000 at the end of his investment
horizon. How much must he invest today, that is, what is the value of x? By applying
the preceding equation manually, we have the following result. Please pay attention
to the negative sign:
>>> -(7000/(1+0.05)**10 + 5000/0.05*(1-1/(1+0.05)**10)*(1+0.05))
-44836.501153005614
The result is the same as when the scipy.pv() function is called; see the
following code:
>>> import scipy as sp
>>> sp.pv(0.05,10,5000,7000,1)
-44836.5011530056
To separate normal annuity from annuity due, we have the following two equations.
For a normal annuity, we have the following equation:
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