Question

A principal of ₹ 40,000 is invested at the rate of 10% for 2 years in compound interest. Find the compound interest and is it greater than the simple interest for the same rate and the same time?

• A. 48400, yes
• B. 48000, yes
• C. 47000, no
• D. 48400, no

Answer 1

The correct option is A

48400, yes

According to the question, interest is only for 2 years

P = ₹ 40,000

In compound interest, interest is calculated annually.
Amount after $1^{st}$ year is $A_1$ = $40,000\times \frac{10}{100}$= ₹ (4,000 + 40,000) = ₹ 44,000
Similarly $A_2=44,000+44,000\times \frac{10}{100}$ = ₹ 48,400

Simple interest (SI) is given by

SI =$\frac{P\times T\times R}{100}$

where P = Principal, T = Time, R = Rate of interest per annum

So, SI =$\frac{PTR}{100}$ = $\frac{40,000\times 10\times 2}{100}$ = ₹ 8,000

$\therefore$ Amount = ₹ 48,000

The simple interest is ₹ 8000 and compound interest is₹ 8400. Therefore, compound interest is greater than the simple interest.