Question

A principal of ₹ 40,000 is compounded annually at the rate of 10% for 2 years. Find the compound interest earned and is it greater than the simple interest earned at the same rate and for the same time period.

• A. ₹ 5400, yes
• B. ₹ 8400, yes
• C. ₹ 7200, no
• D. ₹ 10400, no

Answer 1

The correct option is B ₹ 8400, yes

$\text{Given, Principal, P}=₹40,000\text{Time, T}=2\text{years}\text{Rate of interest, R}=10\%$

We know that,
for a principal P, rate of interest R and time n years,
$\text{amount, A =}P{[1+\frac{R}{100}]}^n$

So,
$A=₹40,000{[1+\frac{10}{100}]}^2$

$A=₹40,000\times \frac{110}{100}\times \frac{110}{100}$

= ₹ 40,000 x 1.1 x 1.1
= ₹ 48,400

Therefore, Compound interest
= Amount - Principal
= ₹ (48,400 - 40,000)
= ₹ 8,400

$\text{Simple interest}=\frac{P\times R\times T}{100}$

$=\frac{40,000\times 10\times 2}{100}$

= ₹ 8,000

Therefore, the compound interest earned is greater than the simple interest earned at the same rate and for the same time.