What is the difference between simple and compound interest 1000 at 10% for 5 years?

The difference between simple and compound interest on Rs. 1,000 for 3 years at 5% p.a. interest is:

1. Rs. 8.4
2. Rs. 10.15
3. Rs. 7.6
4. Rs. 9.2

Answer (Detailed Solution Below)

Option 3 : Rs. 7.6

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∵ Simple interest = (Principal × Rate × Time)/100

⇒ Simple interest = (1000 × 5 × 3)/100 = Rs. 150

Also,

When the interest is compounded annually,

Compound interest = Principal × [(1 + Rate/100)Time – 1]

⇒ Compound Interest = 1000 × [(1 + 5/100)3 – 1] = 1000 × 0.1576 = Rs. 157.6

∴ Required difference = 157.6 – 150 = Rs. 7.6

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Let's discuss the concepts related to Interest and Simple and Compound Both. Explore more from Quantitative Aptitude here. Learn now!

Answer

Verified

Hint: To find the difference between the simple interest and compound interest, first calculate the simple interest and then compound interest then subtract simple interest in compound interest.

Complete step-by-step answer:
In the calculation of compound interest if we take small compounding time then the compound interest will be high as the compounding time will increase and the amount of compound interest will decrease.
Given the value of rate of interest = 10%
Principal = Rs 1000
Time = 4 years
We know that simple interest $ = \dfrac{{PRT}}{{100}}$
On putting the given values we get,
$\Rightarrow$ S.I. $ = \dfrac{{1000 \times 10 \times 4}}{{100}}$
S.I. $ = 400$ Rs
Similarly we will find the compound interest
$\Rightarrow$ We know compound interest = Amount−Principal
and amount is given by
$ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}$
On putting the given values we get
A = \[1000{\left( {1 + \dfrac{{10}}{{100}}} \right)^4}\]

\[ = 1000 \times \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}} \times
\Rightarrow \dfrac{{110}}{{100}} \times \dfrac{{110}}{{100}}\]
\[ = 1464.10\] Rs.
\[C.I. = 1464.10 - 1000 = 464.10\] Rs.
Now we will find the difference between C.I. and S.I.
Difference between C.I and S.I $464.10 - 400 = 64.10$ Rs.

Note: Compound interest is always higher than the simple interest for the same time period and same rate of interest only except the first year. In first year CI and SI are the same.

Answer

Verified

Hint: We will first start by using the fact that simple interest on a principal P at a rate R for time T is $\dfrac{P\times R\times T}{100}$ whereas the compound interest on a principal P at a rate R for time T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Then we will find its difference to find the answer.Complete step-by-step solution -
Now, we have been given a principal amount of Rs. 1000, the interest is 10% per annum for a period of 4 years.
Now, we know that the simple interest on a principal P at a rate of R for T years is $\dfrac{P\times R\times T}{100}$. So, using this we have simple interest $=\dfrac{1000\times 4\times 10}{100}=Rs.400$.
Now, we know that compound interest on a principal P at a rate R for a period of T is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$.
$\begin{align}
  & =1000{{\left( 1+\dfrac{10}{100} \right)}^{4}}-1000 \\
 & =1000{{\left( 1+\dfrac{1}{10} \right)}^{4}}-1000 \\
 & =464.1 \\
\end{align}$
Hence, the difference between compound interest and simple interest is,
$\begin{align}
  & 464.1-400 \\
 & =64.1 \\
\end{align}$
Hence, the correct option is (D).

Note: It is important to note that we have used a fact that for finding SI on a principal amount P at a rate R for a period of T is $\dfrac{P\times R\times T}{100}$ and for compound interest for the same, conditions is $P{{\left( 1+\dfrac{R}{100} \right)}^{T}}-P$. Also, it is important to remember that compound interest is always greater than simple interest.

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