What is the difference (in ₹) between the compound interest, when interest is compounded 6-monthly, and the simple interest on a sum of ₹20,000 for 1$$\frac{1}{2}$$ year at 10% p.a.?

Given, Principal = ₹20,000

Time = $$1\frac{\ 1}{2}\ yr$$

R = 10%

Simple Interest = $$\frac{p\times\ r\times\ t}{100}=\frac{20000\times\ 10\times\ 1.5}{100}=₹3000$$

Compound Interest = $$p\left(1+\frac{r}{100}\right)^n-p$$

For compounded 6-monthly,

Time (t) = $$1.5\times\ 2=3$$

Rate (r) = $$\frac{r}{2}=\frac{10}{2}=5$$

 = $$20000\left(1+\frac{5}{100}\right)^3-20000$$

= $$20000\times\ \frac{21}{20}\times\ \frac{21}{20}\times\ \frac{21}{20}-20000$$

= 23152.5 - 20000 = ₹3152.5

Required Difference = ₹3152.5 - ₹3000 = ₹152.5

Hence, Option D is correct.