Question

A principal of ₹40,000 is compound annually at a rate of 10% for 2 years. What is the compound interest?

Is compound interest greater than the simple interest for the same rate and at the same time?

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

Answer 1

The correct option is A

48400, yes

Given

T = 2 years

P = ₹40,000

Compound interest is calculated annually.

For 1st year, Interest = $\frac{PTR}{100}$ = $40,000\times 1\times \frac{10}{100}$
Amount after $1^{st}$ year is $A_1$ = Principal(P)+ Interest = ₹(4,000 + 40,000) = ₹44,000

In compound interest for the 2 nd year the amount of 1 st year becomes the principal.

Interest for the 2nd year = $\frac{PTR}{100}$ = $44,000\times 1\times \frac{10}{100}$ = ₹4400

Compound Interest = Total interest for 2 years = ₹4000 + ₹4400 = ₹8400

Amount after 2 years $A_2$ = ₹44000 + ₹4400 = ₹48,400

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

$\therefore$ Amount = Principal (P) + Amount = ₹40,000 + ₹8,000 = ₹48,000

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