Question

When required the following logarithms may be used.
$\log 2=.3010300,\log 3=.4771213$,
$\log 7=.8450980,\log 11=1.0413927$.
Show that money will increase more than a hundredfold in a century at $5$ per cent. compound interest.

Answer 1

Let $P$ be the Principal in pound.

$R$ be the interest rate .

$n$ be the number of year.

$S.I$ be the simple interest.

$D$ be the discount .

$M$ be amount

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

$S.I=P\times R\times n$

$D=\frac{P\times R\times n}{1+Rn}$

Thus,

$M=P{(1+\frac{5}{100})}^{100}$

$M=P{\left(\frac{21}{20}\right)}^{100}$

Taking $\log$ both side .

$\log M=\log P+100\left(\log 21\right)-100\left(\log 20\right)$

$\log M=\log P+2.11898$

$M=P\times {10}^{2.11898}$

Thus $M$ is greater than $P\times 100$