Question

A man borrowed Rs.$25,000$ from a finance company at $20%$ per annum. What amount of money will discharge his debt after $2$ years? Also find the difference between Compound interest and simple interest?

Answer 1

Hint: So basically we have been given principal amount, rate of interest and time. So, use the formula to find simple interest and compound interest. After that find the difference between compound interest and simple interest.

Complete step-by-step answer:
Here principal amount(P)$=$Rs.$25,000$.
Rate per interest(R)$=20%$ per annum.
Time(T)$=2$ years.
Now we have to find simple interest,
Simple interest$=\dfrac{\text{P}\times \text{R}\times \text{T}}{100}$
So substituting above values we get,
Simple interest$=\dfrac{25000\times 20\times 2}{100}$
Simplifying we get,
Simple interest$=$Rs. $10000$
Now let us find compound interest.
For that first we have found Amount(A).
A$=\text{P}{{\left( 1+\dfrac{\text{R}}{100} \right)}^{n}}$
Substituting the values we get,
A$=25000{{\left( 1+\dfrac{20}{100} \right)}^{2}}$
A$=25000{{\left( 1+\dfrac{1}{5} \right)}^{2}}$
A$=25000{{\left( \dfrac{6}{5} \right)}^{2}}$
A$=25000\left( \dfrac{36}{25} \right)$
Again simplifying we get,
A$=$Rs. $36000$
Now, Compound interest$=\text{A-P}$
Again substituting values we get,
Compound interest$=36000\text{-25000}$
Compound interest$=$Rs. $11000$
Difference between compound interest and simple interest$=11000-10000$
Difference between compound interest and simple interest$=$ Rs. $1000$.
Therefore, Rs. $36000$ is the amount of money he will discharge his debt after $2$years.
Also, Difference between compound interest and simple interest Rs. $1000$.

Additional information:
Simple Interest is the method of calculating the interest amount for some principal amount of money. Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept which is used in most of the sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount.
Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from the simple interest where interest is not added to the principal while calculating the interest during the next period. Compound interest finds its usage in most of the transactions in the banking and finance sectors and also in other areas as well.

Note: Simple Interest is the method of calculating the interest amount for some principal amount of money. Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. The major difference between simple and compound interest is that simple interest is based on the principal amount of a deposit or a loan whereas the compound interest is based on the principal amount and interest that accumulates in every period of time.