Question

Find the difference of compound interest and simple interest on $Rs.15,000$ at the same rate of interest $12\frac{1}{2}\%$ p.a for $2$ years.

Answer 1

Given that,

$P=Rs.15,000$

$R=12\frac{1}{2}=\frac{25}{2}$ p.a

$T=2$years

$\because C.I=P{(1+\frac{R}{100})}^n-P$

$⟹C.I=15000{(1+\frac{25}{200})}^2-15000$

$⟹C.I=15000{(1+\frac{1}{8})}^2-15000$

$⟹C.I=15000{\left(\frac{9}{8}\right)}^2-15000$

$⟹C.I=15000\left(\frac{81}{64}\right)-15000$

$⟹C.I=18984.38-15000$

$\therefore C.I=Rs.3,984.38$........(i)

$\because S.I=\frac{PTR}{100}$

$⟹S.I=\frac{15000\times 2\times 25}{2\times 100}$

$⟹S.I=150\times 25$

$\therefore S.I=Rs.3750$...........(ii)

From, (i) & (ii) Required difference $=3984.38-3750=Rs.234.38$