Answer: Rs 486

Solution:

Given,
Simple Interest (SI) = Rs 960
Rate of Interest (R) = 5%
Time (T) = 2 years

To find: Compound Interest compounded (reckoned) half-yearly for 1 year (CI) = ?


We know,
$P = \dfrac{I×100}{R×T}$

$or, P = \dfrac{960 × 100}{5×2}$

$\therefore P = Rs 9600$


And,
$CI =  P \left [ \left ( 1 +  \dfrac{R}{200} \right )^{2T} -1\right ]$

$= P \left [ \left ( 1 + \dfrac{5}{200} \right )^{2×1} - 1 \right ]$

$= P \left [ \left ( \dfrac{205}{200} \right )^2 - 1 \right ]$

$= P \left [ \left ( \dfrac{41}{40} \right )^2 - 1 \right ]$

$= P \left [ \dfrac{168}{1600} - 1 \right ]$

$= P \left [ \dfrac{1681 - 1600}{1600} \right ]$

$= 9600 × \dfrac{81}{1600}$

$= 96 × \dfrac{81}{16}$

$= Rs 486$

Hence, the required compound interest on the same sum at the same rate for 1 year compounded semi-annually is Rs 486.


[Reckon means establish by calculation]

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