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QUESTION

Using the results of question 4, suppose you want to retire in 35
years time with a total pension fund of \pounds250,000 (or
equivalent Euros/Dollars\ldots).

Calculate your pension payments assuming annual compounding,
assuming annual growths of

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\item[(a)]
5\%

\item[(b)]
15\%

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This question should teach you never to be an academic.


ANSWER

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\item[(a)]
$T=35,\ F_T=250,000,\ r=5\%$

Annual compounding:
$d=\frac{250,000\times0.05}{(1.05)^{35}-1}=2767.93$

m-compounding, say $m=2$:
$d=250,000\left\{\frac{\left(1+\frac{0.05}{2}\right)^2-1}{\left(1+\frac{0.05}{2}\right)^{70}-1}\right\}=2732.29$

continuous compounding:
$d=\frac{250,000(e^{0.05}-1)}{(e^{0.05435}-1)}=2695.87$

\item[(b)]
$T=35,\ F_T=250,000,\ r=15\%$

Annual compounding:
$d=\frac{250,000\times0.15}{(1.15)^{35}-1}=283.71$

m-compounding, say $m=2$:
$d=250,000\left\{\frac{\left(1+\frac{0.15}{2}\right)^2-1}{\left(1+\frac{0.15}{2}\right)^{70}-1}\right\}=247.85$

continuous compounding:
$d=\frac{250,000(e^{0.15}-1)}{(e^{0.15\times35}-1)}=213.43$

Note that there is a factor of 10 difference in payments if return
con be increased from 5\% to 15\%. 5\% is probably more likely
over 35 years!

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