What is the difference (in ₹) between the compound interest, when interest is compounded 6-monthly, and the simple interest on a sum of ₹10,000 for 1 1/2 years at 10% p.a.?

Correct option is B

Given:

Principle =₹10,000

Interest =10%

Time = $$1\frac{1}{2}$$​years

Formula Used:

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

Compound Interest = Amount - Interest

Simple Interest =$$\frac{P \times r \times t }{100}$$​​

Solution:

For Compound Interest:

Rate of interest = $$\frac{10}{2}$$  = 5%    (Interest is calculated half-yearly)

Number of half years $$= 1\frac{1}{2 }\times 2 = \frac{3}{2} \times 2$$​ = 3 half-years

Compounded amount = $$10000 \times \left(1+ \frac{5}{100}\right)^{3}$$​​

​$$= 10000 \times \left(\frac{105}{100}\right)^{3}$$​​

​$$= 10000 \times \left(\frac{21}{20}\right)^{3}$$​​

= 11576.25

Compound Interest = 11576.25 - 10000 = ₹1576.25

For Simple Interest:

Rate on Interest = 10%

Time =$$1\frac{1}{2} = \frac{3}{2}$$​years

SI =$$\frac{10000 \times10 \times \frac{3}{2} }{100}$$​​

= ₹1500

Difference in CI and SI = 1576.25 - 1500 = ₹76.25