If the simple interest for 2 years is Rs. 1440, what is the rate of interest ?
This problem involves calculating the rate of interest given the difference between compound interest (CI) and simple interest (SI) over two years, and the SI amount for the same period.
Calculating Interest Rate from CI and SI Difference
We are given:
- Difference between CI and SI for 2 years = Rs. 60
- Simple Interest (SI) for 2 years = Rs. 1440
First, let's find the Simple Interest for one year:
SI for 1 year = $\frac{\text{SI for 2 years}}{2}$
SI for 1 year = $\frac{1440}{2} = \text{Rs. } 720$
The difference between CI and SI for 2 years is equal to the interest charged on the first year's SI for the second year. The formula relating the difference, SI for one year, and the rate (R) is:
Difference = SI for 1 year $\times \frac{R}{100}$
Now, substitute the known values into the formula:
Rs. 60 = Rs. 720 $\times \frac{R}{100}$
To find the rate R, rearrange the equation:
\frac{R}{100} = \frac{60}{720}
\frac{R}{100} = \frac{1}{12}
R = \frac{100}{12}
R = \frac{25}{3}
R = 8\frac{1}{3}\%
Therefore, the rate of interest is $8\frac{1}{3}\%$.
Important Questions from Simple and Compound Both
What is the compound interest (in Rs.) at the rate of 10%, compounded annually, for 3 years on the principal which in 8 years at the rate of 12% per annum gives Rs. 4,800 as simple interest?
A certain sum amounts to Rs. 15,500 in 2 years at 12% p.a. simple interest. If the same sum is compounded half-yearly at 10% per annum for \(1 \frac{1}{2}\) years, what will be the amount received?
The difference in compound interest on a certain sum at 10% p.a. for one year, when the interest is compounded half-yearly and yearly, is Rs. 88.80. What is the simple interest on the same sum for \(1\frac{2}{3}\) years at the same rate?
A sum of Rs. 7500 amounts to Rs. 9075 at 10% p.a, interest being compounded yearly in a certain time. The simple interest (in Rs.) on the same sum for the same time and the same rate is:
A certain sum amounts to Rs.291600 in 2 years and to Rs.314928 in 3 years on compound interest compounded annually. How much will be the simple interest (in Rs.) on Rs.40000 at the same rate for 2 years?
