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:
1500
Calculating Simple Interest from Compound Interest Data
This problem involves two types of interest: compound interest and simple interest. We are given information about a sum of money growing under compound interest and asked to find the simple interest on the same sum for the same time period and rate.
Understanding the Given Information
- Principal sum (P) = Rs. 7500
- Amount after compounding (A) = Rs. 9075
- Rate of interest (R) = 10% per annum
- Compounding Frequency: Yearly
- We need to find the time period (T) first.
- Then, we need to calculate the Simple Interest (SI) for the same P, R, and the calculated T.
Step 1: Finding the Time Period (T)
The formula for the Amount (A) under compound interest compounded yearly is:
\( A = P \left(1 + \frac{R}{100}\right)^T \)
Let's substitute the given values into the formula:
\( 9075 = 7500 \left(1 + \frac{10}{100}\right)^T \)
Simplify the term inside the bracket:
\( 9075 = 7500 \left(1 + 0.1\right)^T \)
\( 9075 = 7500 (1.1)^T \)
Now, isolate the term with T by dividing both sides by 7500:
\( \frac{9075}{7500} = (1.1)^T \)
Calculate the value on the left side:
\( \frac{9075}{7500} = \frac{121 \times 75}{100 \times 75} = \frac{121}{100} = 1.21 \)
So, we have:
\( 1.21 = (1.1)^T \)
We know that \( (1.1)^2 = 1.1 \times 1.1 = 1.21 \). Comparing this with the equation, we find T.
\( (1.1)^2 = (1.1)^T \)
Therefore, the time period \( T = 2 \) years.
Step 2: Calculating Simple Interest (SI)
Now that we have the time period (T = 2 years), we can calculate the simple interest on the original sum (P = Rs. 7500) at the same rate (R = 10% p.a.) for this time.
The formula for Simple Interest (SI) is:
\( SI = \frac{P \times R \times T}{100} \)
Substitute the values:
\( SI = \frac{7500 \times 10 \times 2}{100} \)
Perform the multiplication in the numerator:
\( SI = \frac{7500 \times 20}{100} \)
Now, divide by 100:
\( SI = \frac{150000}{100} \)
\( SI = 1500 \)
The simple interest on the sum for the same time and rate is Rs. 1500.
Final Answer
The simple interest on Rs. 7500 for 2 years at 10% p.a. is Rs. 1500.
| Particulars | Value |
|---|---|
| Principal (P) | Rs. 7500 |
| Amount (CI) | Rs. 9075 |
| Rate (R) | 10% p.a. |
| Time (T) - Calculated | 2 Years |
| Simple Interest (SI) - Calculated | Rs. 1500 |
Revision Table: Interest Formulas
| Concept | Formula | Notes |
|---|---|---|
| Simple Interest (SI) | \( SI = \frac{P \times R \times T}{100} \) | Interest calculated only on the principal amount. P=Principal, R=Rate (% per annum), T=Time (in years). |
| Amount (A) with Simple Interest | \( A = P + SI \) or \( A = P \left(1 + \frac{RT}{100}\right) \) | Total amount after earning simple interest. |
| Amount (A) with Compound Interest (yearly) | \( A = P \left(1 + \frac{R}{100}\right)^T \) | Interest is added to the principal at the end of each year and earns interest in subsequent years. |
| Compound Interest (CI) | \( CI = A - P \) or \( CI = P \left[ \left(1 + \frac{R}{100}\right)^T - 1 \right] \) | The difference between the amount and the principal. |
Additional Information on Simple and Compound Interest
Simple interest is the most basic form of interest calculation. It is calculated only on the initial principal amount for the entire duration. The interest earned in previous periods does not add to the principal for calculating interest in the current period.
Compound interest, on the other hand, is calculated on the principal amount and also on the accumulated interest of previous periods. This means that the principal effectively increases over time, leading to exponential growth in the amount. The frequency of compounding (yearly, half-yearly, quarterly, etc.) affects the total interest earned.
In this problem, we first used the compound interest formula to find the unknown time period, as the amount after compounding was given. Once the time was determined, we applied the simple interest formula using the same principal, rate, and the calculated time period to find the required simple interest value. Understanding both formulas and how to manipulate them to find different variables like time or rate is crucial for solving such problems.
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 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?
The difference between compound interest and simple interest on x at 15% per annum for 2 years is 9. What is the value of x?
