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Saurabh invests Rs. 48,000 for 7 year at \[10\% \] per annum compound interest. Calculate: The interest for the first year.
A.Rs. 4800
B.Rs. 4900
C.Rs. 5000
D.Rs. 5100

Last updated date: 25th Jun 2024
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Hint: Here we have to calculate the simple interest for the given amount for one year. We will substitute the given values in the formula of simple interest and simplify the expression to get the required interest for the first year.

Formula used:
Simple interest \[ = \dfrac{{PRT}}{{100}}\] where, \[P\] is the principal amount, \[R\] is the rate of interest and \[T\] is the time period.

Complete step-by-step answer:
Here, principal amount is Rs. 48,000 i.e. \[P = Rs.48000\] and rate of interest is \[10\% \] i.e. \[R = 10\% \].
We will find the interest on the principal amount for the first year. Therefore, time will be 1 year i.e. \[T = 1{\text{year}}\]. We know that the compound interest on an amount for one year is equal to the simple interest on that amount for one year. Therefore, we get
Interest for one year \[ = \dfrac{{PRT}}{{100}}\]
Substituting \[P = Rs.48000\], \[R = 10\% \] and \[T = 1{\text{year}}\] in the above equation, we get
Interest for one year \[ = \dfrac{{48000 \times 10 \times 1}}{{100}}\]
Interest for one year \[ = Rs.4800\]
Hence the interest for the first year on the amount Rs. 48,000 is Rs. 4800.
So, option A is the correct option.

Note: Here we should note that while calculating the interest we should take the rate of interest in percentage in the formula of the interest. In simple interest, the interest per year remains constant over the period of time but in case of the compound interest, interest per year varies and it goes on increasing over the period of time. Interest is generally used in financial services. Interest can be yearly or monthly or quarterly or semiannually.
Formula of the compound interest, compound interest \[ = P{\left( {1 + \dfrac{R}{{100}}} \right)^T}\] where, \[P\] is the principal amount,\[ R\] is the rate of interest and \[T\] is the time period.