Question

When required the following logarithms may be used.
$\log 2=.3010300,\log 3=.4771213$,
$\log 7=.8450980,\log 11=1.0413927$.
A man borrows $600$ pounds from a money-lender, and the bill is renewed every half-year at an increase of $18$ per cent.: what time will elapse before it reaches $6000$ pounds? Given $\log 118=2.071882$.

Answer 1

$A=P(1+\frac{R}{100}{)}^n$

$6000=600(1+0.18{)}^n=600(1.18{)}^n$

$\Rightarrow \log 10=n\log 1.18$

$\Rightarrow n=\frac{1}{\log 1.18}=13.91$ cycles.

As it is compounded half yearly, Time $=\frac{13.91}{2}=7$ years.