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Calculate the amount and the compound interest on Rs.12,000 in 2 years and at 10% per year.
A. Rs.14,520 and Rs.2,520
B. Rs.14,000 and Rs.2,000
C. Rs.13,520 and Rs.2,820
D. Rs.17,520 and Rs.2,120

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Last updated date: 29th Mar 2024
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MVSAT 2024
Answer
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Hint: The given problem is related to compound interest. When the principal amount R is given, the amount after n compounding at a rate of R% is given by the formula:
\[A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}\]
Where, A=final amount.
P=initial amount.
r=interest rate.
n=number of periods elapsed.
The compound interest can be calculated as: Compound interest= A – P
Where, A=final amount.
P=initial amount.

Complete step-by-step answer:

In the question, we are given that,
P=12000, R=10 percent per year, n=2
We know, the formula for amount after n compounding at the rate of R% p.a. is given as : \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}\], where : A=final amount, P=initial amount, r=interest rate, and n=number of periods elapsed.
So, we will substitute P, R, n in the formula \[A=P{{\left( 1+\dfrac{R}{100} \right)}^{n}}\]
Finding the amount:
\[\Rightarrow A=12000{{\left( 1+\dfrac{10}{100} \right)}^{2}}\]
\[\Rightarrow A=12000{{\left( \dfrac{11}{10} \right)}^{2}}\]
\[\Rightarrow A=120(121)=14,520\]
Therefore, the amount is Rs.14,520 . Now, we will find the compound interest. We know, Amount = Principal + Interest. So, Interest = Amount – Principal, i.e. Compound interest= A – P .
We have Amount = Rs. 14,520 , Principal = Rs. 12,000.
So, Compound interest = 14520-12000
=2520
Therefore, compound interest for the amount is Rs.14,520 is Rs.2520
Hence, the correct option is option (A).

Note: We can do the sum by simply checking the following condition:
We know that, compound interest = final amount- principal amount
That is, final amount – compound interest= 12000. Now check the condition by substitute the options in this formula. Only option d satisfies here (this helps to do the problem quickly in the exams).