Question

The interest earned on $Rs.20000$ at the rate of $20\%$ per annum for $1.5$ years if compounded semi annually is how much more than the simple interest earned on the same amount with the same rate of interest for the same period.

Answer 1

Given principal amount $P=Rs.20,000$
Rate of interest, $R=20\%$ and time, $T=1.5$ years.
Compound interest formula, $A=P(1+\frac{R}{n\times 100}{)}^{nT}$
Where $n$ is the number of times interest compounds annually.
When the interest compounded semi annually then Amount after $1.5$ years $A=20,000(1+\frac{20}{2\times 100}{)}^{2\times 1.5}$ [Since, $n=2$]
$=20,000(1+0.1{)}^3$
$=20,000(1.1{)}^3$
$=20,000\times 1.331$
Therefore, Amount $A=Rs.26,620$
Therefore, C.I $=A-P$
C.I $=26,620-20000$
C.I$=Rs.6,620$

Simple interest: $S.I.=\frac{P\times T\times R}{100}$
$\Rightarrow S.I.=\frac{20,000\times 1.5\times 20}{100}$
$=Rs.6,000$
$\therefore C.I.-S.I=6,620-6,000=Rs.620$