Question

Calculate the amount and the compound interest on Rs. 5,000 in 2 years, if the rates of interest for the successive years are 8% and 10% respectively.

Answer 1

Hint: For finding the amount, we generally use the formula, $A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)\left( 1+\dfrac{{{R}_{3}}}{100} \right).....$, where P is the principal amount, ${{R}_{1}}$ is the rate of interest for the first term, ${{R}_{2}}$ is the rate of interest for the second term, and similarly ${{R}_{4}},{{R}_{5}},{{R}_{6}},...$ are the rates of interest for the respective terms. Here, the term actually means the time period. So, in our question, we have been given 2 years, so we will use the formula, $A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)$. Then, to find the compound interest, we will use the formula, Compound interest (CI) = Amount (A) – Principal (P).

Complete step-by-step answer:
It is given in the question that we have to find the amount and the compound interest on Rs. 5,000 in 2 years, if the rates of interest for the successive years are 8% and 10% respectively.
So, from the question we get the following data,
Principal amount, P = Rs. 5000
Rate of interest for the first year, ${{R}_{1}}$ = 8%
Rate of interest for the second year, ${{R}_{2}}$= 10%
Since we have to find the compound interest and we know that in compound interest, the interest is compounded annually, we will consider 1 term as 1 year.
Now, we know that if there are n number of years and we have to invest p, the principal amount with the rate of interest for the first year as ${{R}_{1}}$ and for the second year as ${{R}_{2}}$, and so on, we can find the amount using the formula, $A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)\left( 1+\dfrac{{{R}_{3}}}{100} \right).....\left( 1+\dfrac{{{R}_{n}}}{100} \right)$.
So, in our question the number of years is given as 2. So, we will get the general equation to find the amount as,
$A=P\left( 1+\dfrac{{{R}_{1}}}{100} \right)\left( 1+\dfrac{{{R}_{2}}}{100} \right)$
So, on substituting the values of P = Rs. 5000, ${{R}_{1}}$ = 8% and ${{R}_{2}}$= 10% in the above equation, we will get,
$A=5000\left( 1+\dfrac{8}{100} \right)\left( 1+\dfrac{10}{100} \right)$
On taking LCM of the terms inside the brackets, we get,
\[A=5000\left( \dfrac{100+8}{100} \right)\left( \dfrac{100+10}{100} \right)\]
On solving further, we get,
\[\begin{align}
  & A=5000\left( \dfrac{108}{100} \right)\left( \dfrac{110}{100} \right) \\
 & A=Rs.5940 \\
\end{align}\]
Thus, we get the amount as Rs. 5940.
Now, to find the compound interest, we will use the formula, Compound interest (CI) = Amount (A) – Principal (P). So, we can write,
CI = A – P
CI = Rs. 5940 – Rs. 5000
CI = Rs. 940
Thus, we get the compound interest as Rs. 940.
Therefore, we get the amount as Rs. 5940 and the compound interest as Rs. 940 for two years.

Note:Some students may mistake while finding the compound interest, they may write the formula as, CI = A + P instead of CI = A – P, so the students must be careful while writing the formula. Also, if the interest is calculated half yearly, then the rate of interest becomes half of the given rate.