Question

Find the difference between S.I. and C.I. on Rs. 5000 for 2 years at $6\%$ per annum.

Answer 1

Hint: We need to find the knowledge about simple interest and compound interest. Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments. The formula for the simple interest is $\text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{P\times n\times r}{100}$ where P = principal value, n = number of years, r = the rate of interest. Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods.

Complete step-by-step answer:
The formula for compound interest is $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ where A = amount of previous value, P = principal value, n = number of years, r = the rate of interest.
We need to understand the simple interest and compound interest
Simple interest is determined by multiplying the daily interest rate by the principal by the number of days that elapse between payments.
The formula for the simple interest is given as follows,
$\text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{P\times n\times r}{100}..................(i)$ ,
where P = principal value,
n = number of years
r = the rate of interest.
Compound interest is interest calculated on the initial principal which also includes all the accumulated interest from the previous periods.
The formula for compound interest is as follows
$A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}...........(ii)$
where A = amount of previous value,
P = principal value,
n = number of years,
r = the rate of interest.
Now, we need to find the simple interest and the compound interest of the situation we have been given,
We have, P = Rs. 5000,
n = 2 years,
r = $6\%$,
Substituting in the above equation we get,
$\begin{align}
  & \text{Simple interest}\left( \text{S}\text{.I}\text{.} \right)\text{ = }\dfrac{5000\times 2\times 6}{100} \\
 & =600
\end{align}$
Therefore, the simple interest is Rs. 600.
Now we need to substitute the same values in the formula for compound interest
$A=5000{{\left( 1+\dfrac{6}{100} \right)}^{2}}$
Solving the equation, we get,
$\begin{align}
  & A=5000{{\left( 1.06 \right)}^{2}} \\
 & =5000\times 1.1236 \\
 & =5618
\end{align}$
The compound interest is given by C.I. = Amount – principal amount.
Therefore, by substituting the values, we get,
C.I. = 5618 – 5000 = 618.
Therefore, the compound interest is Rs. 618.
We need to find the difference between simple interest and compound interest.
The difference between simple and compound interest is 618 – 600 = RS. 18.

Note: The answer we get from the compound interest formula is the amount and not the compound interest. We can find the compound interest by subtracting the principal from principal value. We do not need to worry about the sign while finding the difference between simple interest and compound interest.