The difference between Compound Interest and Simple Interest on R…

MCQ

The difference between Compound Interest and Simple Interest on Rs. $24,000$ at $20 \%$ per annum for $2$ years is:

A
Rs. $480$
B
Rs. $954$
✓
Rs. $960$
D
Rs. $879$

✓

Answer

Correct option: C.

Rs. $960$

Given that. $P =$ Rs. $24,000$ $R = 20 \%$ per annum $T$ or $n$ = $2$ years
Now, for simple interest:
$\text{SI}=\text{SI}=\frac{\text{P}\times\text{R}\times\text{T}}{100}=\frac{24000\times20\times2}{100}=9,600$
For $CI$, we first calculate amount$(A)$
$\text{A}=\text{P}\Big[1+\frac{\text{R}}{100}\Big]^\text{n}$
$\Rightarrow\text{A}=24000\Big[1+\frac{20}{100}\Big]^2$
$\Rightarrow\text{A}=24000\Big[1+\frac{120}{100}\Big]^2$
$\Rightarrow\text{A}=34560$
Now compound interest $(CI) = A - p = 34650 - 24,000 = 10,560$
Clearly, difference between $CI$ and $Si$ = Rs. $(10,560 - 9,600)$ = Rs. $960$

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