What is the difference between the compound interests on ₹8,000 for 1 year at 6% per annum compounded yearly and half-yearly?

Correct option is A

Given:

Rate of interest = 6%

Time = 1year

Principle = ₹8,000

Formula Used:

Compounded Amount =$$Principle \times \left(1+ \frac{r}{100}\right)^{t}$$ 

Compound interest = Compounded Amount - Principle

​​​Solution:

When interest is compounded yearly

Compound Interest = $$8000 \times \left(1+ \frac{6}{100}\right)^{1} - 8000$$​​

​$$= 8000\left(\frac{106}{100}\right) - 8000$$​​

= 8480 - 8000

= ₹480

If interest is calculated half yearly, then

Rate of interest will be =$$\frac{6}{2} =3$$​%

Time will be t = $$1\times2 = 2$$ (as interest is half yearly)

​$$CI= 8000 \times \left(1+ \frac{3}{100}\right)^{2} - 8000$$​​

​$$= 8000\left(\frac{103}{100}\right)^{2} - 8000$$​​

= 8487.2 - 8000

= ₹487.2

Difference in interest accrued on both schemes = 487.2 - 480 = ₹7.2