Question

A principal of ₹40,000 is compounded annually at the rate of 10% for 2 years. Calculate the compound interest. Is it greater than the simple interest earned at the same rate and for the same time period?​
[5 marks]

Answer 1

For compound interest,
A = P $(1+\frac{r}{100})$${}^t$
[0.5 marks]

Here,
A = 40,000$(1+\frac{10}{100}$)${}^2$
⇒ A = 40,000$(\frac{11}{10}$)${}^2$
⇒ A = 40,000$(\frac{121}{100}$)
⇒ A = 400 $\times$ 121
⇒ A = ₹48,400
[2 marks]

So, compound Interest = ₹48,400 $-$ ₹40,000 = ₹8,400
[0.5 marks]

Now, simple Interest = $\frac{(P\times r\times t)}{100}$
[0.5 marks]

So, Simple Interest = $\frac{(40000\times 10\times 2)}{100}$
Simple Interest = $400\times 10\times 2$ = ₹8,000
[1 mark]

So, compound interest (₹8,400) is more than simple interest (₹8,000) by ₹400 at the same rate and for same period.
[0.5 marks]