Question

What principal will amount to Rs. 9856 in two years, if the rates of interest for successive years are 10% and 12% respectively?

Answer 1

Hint: In order to solve this question, we will first consider the principal as P and then we will apply the formula of 1 year and then we will again apply simple interest on the obtained amount for next year and then we will equate the amount to Rs. 9856 and solve to get the value of P or our answer. We will use the formula of simple interest, $I=\dfrac{PRT}{100}$, where P represents the principal amount, R represents the rate and T represents the time.

Complete step-by-step answer:

In this question, we have been asked to find the principal that will amount to Rs. 9856 after the interest of 2 years for interest rate as 10% and 12%, for successive years. To solve this question, we will first consider the principal amount for which the interest is calculated for 2 years as P.
Now, we know that simple interest is always calculated by $I=\dfrac{PRT}{100}$, where P represents the principal amount, R represents the rate and T represents the time. So, let us say I’ is the interest obtained after the interest of one year at a rate of 10% on the principal amount and then let us consider I as the final interest obtained after an year at a rate of 12% on the amount obtained after interest I’.
Now, for the first year, we can say,
P = P, R = 10% and T = 1 year. So, we get the interest, I’ as,
$\begin{align}
  & I'=\dfrac{P\times 10\times 1}{100} \\
 & I'=0.1P \\
\end{align}$
So, we can say that the interest obtained in the first year is 0.1P. So, we can say that the amount obtained after the interest of 1 year is P + 0.1P = 1.1P.
Now, we will calculate the amount obtained on the 1.1P amount at a rate of 12% for 1 year. So, we get,
$\begin{align}
  & I=\dfrac{1.1P\times 12\times 1}{100} \\
 & I=0.132P \\
\end{align}$
So, we can say that the final amount obtained after the interest of the second year is 1.1P + 0.132P = 1.232P.
Now, we have been given that the final amount obtained after the interest of 2 years is Rs. 9856. So, we can say that,
1.232P = 9856
$\begin{align}
  & P=\dfrac{9856}{1.232} \\
 & P=Rs.8000 \\
\end{align}$
Hence, we can say that Rs. 8000 will amount to Rs. 9856 in two years, when the rates of interest for successive years are 10% and 12% respectively.

Note: While solving this question, the possible mistake we can make is by not calculating the final amount after the interest of each year and solving the question further with the interest as the final amount which will give us the wrong answer and we may lose our marks. Also, some students add 10% and 12% and take 22% as the rate of interest and then apply it in the formula and find the answer, but this is wrong and should be avoided.