If a sum of ₹6,70,000 is invested for a year at 2% per annum compounded half yearly, then find the compound interest.

Correct option is B

Given:

Principal (P) = ₹6,70,000

Rate of interest (R) = 2% per annum

Time (T) = 1 year

The interest is compounded half-yearly.

We need to find the compound interest.

Formula Used: 

For half-yearly time

Compounded Amount, A = $$P \left(1 + \frac{R}{2 \times 100}\right)^{2T}$$​​

C I = A - P

Solution:

Substituting the given values into the formula:

A = $$6,70,000 \left(1 + \frac{2}{2 \times 100}\right)^{2 \times 1}$$​​

​$$= 6,70,000 \left(1 + \frac{1}{100}\right)^2$$​​

​$$= 6,70,000 \left(\frac{101}{100}\right)^2$$​​

​$$= 6,70,000 \times \left(\frac{101}{100}\right)^2$$​​

​$$= 6,70,000 \times \frac{10201}{10000}$$​​

= 6,83,467

Now, 

Compound interest = 6,83,467 - 6,70,000 = ₹13,467