Question

The present value of $672$ pounds due in a certain time is $126$ pounds; if compound interest at $4\frac{1}{6}$ per cent. be allowed, find the time; having given
$\log 2=.30103,\log 3=.44712$.

Answer 1

Here $r=\frac{4\frac{1}{6}}{100}=\frac{1}{24}$, and $R=\frac{25}{24}$.
Let $n$ be the number of years; then
$672=126{\left(\frac{25}{24}\right)}^n$;
$\therefore n\log \frac{25}{24}=\log \frac{672}{126}$,
or $n\log \frac{100}{96}=\log \frac{16}{3}$;
$\therefore n(\log 100-\log 96)=\log 16-\log 3$
$n=\frac{4\log 2-\log 3}{2-5\log 2-\log 3}$
$n=\frac{.72700}{.01773}=41$, very nearly;
thus the time is very nearly $41$ years.