The simple interest on a sum of money for 2 years at 4% per annum is ₹ 340. The compound interest on this sum for one year payable half-yearly at the same rate is:

1. ₹ 170.70

2. ₹ 107.70

3. ₹ 171.70

4. ₹ 270.70

Given,

I = ₹ 340

R = 4%

T = 2 years

Let sum of money be ₹ P.

By formula,

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

$\Rightarrow 340 = \dfrac{P \times 4 \times 2}{100} \\[1em] \Rightarrow 340 = \dfrac{P \times 8}{100} \\[1em] \Rightarrow P = \dfrac{340 \times 100}{8} \\[1em] \Rightarrow P = ₹ 4,250.$

Given, interest is compounded half-yearly.

By formula,

$A = P\Big(1 + \dfrac{r}{2 \times 100}\Big)^{2 \times n}$

Substituting values we get :

$\Rightarrow A = 4250 \Big(1 + \dfrac{4}{2 \times 100}\Big)^{2 \times 1} \\[1em] \Rightarrow A = 4250 \Big(\dfrac{200 + 4}{200}\Big)^2 \\[1em] \Rightarrow A = 4250 \Big(\dfrac{204}{200}\Big)^2 \\[1em] \Rightarrow A = 4250 \Big(1.02\Big)^2 \\[1em] \Rightarrow A = 4250 \times 1.0404 \\[1em] \Rightarrow A = ₹ 4,421.7$

Compound interest = Amount - Principal = ₹ 4,421.7 - ₹ 4,250 = ₹ 171.70.

Hence, option 3 is correct option.