Question

Shikha invested Rs$6,400$ for $3$ years at the rate of $10\%$ per annum compounder annually. Sneha invested the same mount at the same rate for the same time but on simple interest. Who gets more interest and by how much?

• A. Sneha, Rs.$198.40$
• B. Sneha, Rs.$146.50$
• C. Shikha, $146.50$
• D. Shikha, $198.40$

Answer 1

Answer: (D)

Shikha, $198.40$

$SimpleInterest=SI=\frac{PNR}{100}$

$CompoundInterest=CI=P[{(1+\frac{R}{100})}^N-1]$

where $P$ is the principal amount, $N$ is the number of years and $R$ is annual rate of interest.

Here, for both :

$P=Rs.6400$

$N=3years$

$R=10\%p.a.$

$1)Shikha:$

Interest is compounded annually.

$Interest=6400[{(1+\frac{10}{100})}^3-1]=6400({1.1}^3-1)=6400\times 0.331=Rs.2118.40$

$2)Sneha:$

Interest is simple.

$Interest=\frac{6400\times 3\times 10}{100}=Rs.1920.00$

So, Shikha gets more interest than Sneha.

The difference in interests = $2118.40-1920.00=Rs.198.40$

$\therefore$ The answer is $\left[D\right]$.