What is the difference between the compound interest, when interest is compounded 5-monthly, and the simple interest on a sum of ₹12,000 for $$1\frac{1}{4}$$ years at 12% per annum?

$$simple\ interest=\frac{12000\times5\times12}{4\times100}$$

$$= 30\times60$$

= 1800    Eq.(i)

Here the interest is 12% per annum. It means 12% = 12 months

1% = 1 months

$$\frac{5}{4}\ years\ =\ \frac{5}{4}\ \times\ 12\ months=15\ months$$

15% = 15 months

interest is compounded 5-monthly. It means that 5% in each 5 months.

compound interest = 12000 of (100+5)% of (100+5)% of (100+5)% - 12000

= 12000 of 105% of 105% of 105% - 12000

$$=12000\times1.05\times1.05\times1.05 - 12000$$

$$=12000\times1.157625-12000$$

$$=12000\times\left(1.157625-1\right)$$

$$=12000\times0.157625$$

= 1891.5    Eq.(ii)

Eq.(ii) - Eq.(i)

difference = 1891.5-1800

= ₹91.5