The problem asks for the principal sum invested when the difference between compound interest (CI) and simple interest (SI) over 2 years is given, along with the interest rate.
Calculating Principal from Interest Difference
We are given:
- Interest Rate (R) = 4% per annum
- Time (T) = 2 years
- Difference between CI and SI = ₹47
The formula for the difference between compound interest and simple interest for 2 years is:
\begin{equation*} \text{Difference} = P \times \left(\frac{R}{100}\right)^2 \end{equation*}
Where P is the principal sum.
Solving for the Principal Sum (P)
Substitute the given values into the formula:
\begin{equation*} 47 = P \times \left(\frac{4}{100}\right)^2 \end{equation*}
Simplify the rate fraction:
\begin{equation*} \frac{4}{100} = \frac{1}{25} \end{equation*}
Now, substitute this back into the equation:
\begin{equation*} 47 = P \times \left(\frac{1}{25}\right)^2 \end{equation*}
\begin{equation*} 47 = P \times \frac{1}{625} \end{equation*}
To find P, rearrange the equation:
\begin{equation*} P = 47 \times 625 \end{equation*}
Calculate the final value:
\begin{equation*} P = 29,375 \end{equation*}
Therefore, the sum invested in each case is ₹29,375.
Important Questions from Simple and Compound Intrest
The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. The rate of interest per annum is?
A sum of Rs. 2000 amounts to Rs. 4000 in two years at compound interest. In how many years does the same amount becomes Rs. 8000?
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, the compound interest on the same at the same rate and for the same time is:
- Amit invested equal amounts at simple interest and compound interest, compounded annually, for 2 years at the same rate of 4% per annum. In the end, he found a difference of ₹53 between the two interests earned. What was the amount (in ₹) invested in each case?
- The simple interest on a certain sum for $2\frac{6}{7}$ years at the rate of 7.7% per annum is ₹1,188.
What will be the amount payable on the same sum at the rate of 8.5% per annum simple interest in $4\frac{5}{9}$ years?
