Question

Find the difference between the simple interest and compound interest(to the nearest integer) on Rs. $16,000$ for $1\frac{1}{2}$ years at $5\%$ per annum, compound interest being reckoned half-yearly.

Answer 1

$P=16000$ per month , $T=1.5$ , $R=5\%$

For interest being calculated half-yearly,

Compound Interest$=P{(1+\frac{R}{200})}^{2T}-P$

$=[16000{(1+\frac{5}{200})}^{2\times 1.5}-16000]$

$=16000\left[\right(1+\frac{5}{200}{)}^3-1]$

$=16000\left[\right(1.025{)}^3-1]$

$=Rs.1230.25$

Simple interest $=\frac{PR\left(2T\right)}{200}$

$\therefore$ SI $=\frac{16000\times 5\times 3}{2\times 100}=Rs.1200$

Hence, CI-SI$=Rs.1230.25-Rs.1200=Rs.30$