Question

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

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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.

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 $= Rs.4800$
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.