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Question #cf901

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Aug 1, 2016

$50.67796$ $50.67796$ years

Explanation:

An investment of $I$ $I$ at an annual (compound) rate of $r$ $r$ for a period of $n$ $n$ years yields
$XXX v = I \cdot {(1 + r)}^{n}$ $color(white)("XXX")v=I*(1+r)^n$

We are told
$XXX v = 2467174$ $color(white)("XXX")v=2467174$ (forints)
$XXX r = 7 % = 0.07$ $color(white)("XXX")r=7%=0.07$ and
$XXX I = 80000$ $color(white)("XXX")I=80000$ (forints)

Therefore
$XXX 80000 \cdot {(1.07)}^{n} = 2467174$ $color(white)("XXX")80000 * (1.07)^n=2467174$
or
$XXX {(1.07)}^{n} = \frac{2467174}{80000}$ $color(white)("XXX")(1.07)^n=2467174/80000$

Taking the ${log}_{1.07}$ $log_(1.07)$ of both sides (use a calculator)
$XXX n = {log}_{1.07} (\frac{2467174}{80000}) = 50.67796$ $color(white)("XXX")n=log_1.07 (2467174/80000)=50.67796$

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