The compound interest on a certain sum of money at 5% p.a. for two years is ₹ 246. The simple interest on the same sum for three years at 6% p.a. will be:

1. ₹ 432

2. ₹ 430.50

3. ₹ 432.75

4. ₹ 431.75

Given,

I = ₹ 246

R = 5%

n = 2 years

$A = P\Big(1 + \dfrac{r}{100}\Big)^{n}$

Compound interest = Amount - Principal

$CI = P\Big(1 + \dfrac{r}{100}\Big)^{n} - P$

$\Rightarrow 246 = P \Big(1 + \dfrac{5}{100}\Big)^{2} - P \\[1em] \Rightarrow 246 = P \Big(\dfrac{100 + 5}{100}\Big)^2 - P \\[1em] \Rightarrow 246 = P \Big(\dfrac{105}{100}\Big)^2 - P \\[1em] \Rightarrow 246 = P [(1.05)^2 - 1] \\[1em] \Rightarrow 246 = P [1.1025 - 1] \\[1em] \Rightarrow 246 = 0.1025P \\[1em] \Rightarrow \dfrac{246}{0.1025} = P\\[1em] \Rightarrow P = ₹ 2,400.$

For calculating Simple interest,

P = ₹ 2,400

R = 6%

T = 3 years

I = $\dfrac{P \times R \times T}{100}$

$\Rightarrow I = \dfrac{2400 \times 6 \times 3}{100} \\[1em] \Rightarrow I = \dfrac{43200}{100} \\[1em] \Rightarrow I = ₹ 432$

Hence, option 1 is correct option.