The compound interest on a certain sum of money at 5% per annum for two years

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Question

The compound interest on a certain sum of money at $5 %$ per annum for two years is ₹246. Calculate the simple interest on the same sum for three years at $6 %$ per annum.

Options:

A . ₹430

B . ₹432

C . ₹442

D . ₹452

Answer: Option B
:
B

$We know that, C . I = P [{(1 + \frac{r}{100})}^{n} - 1] where P is the principal, r is the rate of interest and t is the time period.$
$Hence, 246 = P [{(1 + \frac{5}{100})}^{2} - 1]$

$246 = P [(\frac{21}{20}) \times (\frac{21}{20}) - 1] 246 = P \times (\frac{41}{400})$

$\Rightarrow P = \frac{246 \times 400}{41} = ₹ 2400$

$Now, P= ₹ 2400, r = 6 % per annum and t = 3 years$

$S . I = \frac{P \times r \times t}{100} = \frac{2400 \times 6 \times 3}{100} = ₹ 432$

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