A sum of Rs. 5,345, when invested at a certain rate of simple interest per annum for 10 years, earns an interest of Rs. 2,672.50 on maturity. What is the rate of simple interest per annum?
5%
Calculating Simple Interest Rate Per Annum
This question asks us to find the annual rate of simple interest given the principal amount, the time period, and the total simple interest earned.
Understanding Simple Interest
Simple interest is calculated only on the principal amount. It does not compound, meaning the interest earned in previous periods does not earn interest in subsequent periods. The formula for simple interest is:
\( \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \)
Where:
- \( \text{SI} \) is the Simple Interest
- \( \text{P} \) is the Principal amount
- \( \text{R} \) is the Rate of Interest per annum (in percentage)
- \( \text{T} \) is the Time period (in years)
Identifying the Given Values
From the question, we are given the following information:
- Principal amount (\( \text{P} \)) = Rs. 5,345
- Time period (\( \text{T} \)) = 10 years
- Simple Interest earned (\( \text{SI} \)) = Rs. 2,672.50
We need to find the Rate of Interest (\( \text{R} \)) per annum.
Rearranging the Formula to Find the Rate
To find the rate (\( \text{R} \)), we can rearrange the simple interest formula:
\( \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \)
Multiply both sides by 100:
\( \text{SI} \times 100 = \text{P} \times \text{R} \times \text{T} \)
Divide both sides by \( \text{P} \times \text{T} \):
\( \text{R} = \frac{\text{SI} \times 100}{\text{P} \times \text{T}} \)
Calculating the Simple Interest Rate
Now, we substitute the given values into the rearranged formula:
\( \text{R} = \frac{2672.50 \times 100}{5345 \times 10} \)
First, calculate the numerator:
\( 2672.50 \times 100 = 267250 \)
Next, calculate the denominator:
\( 5345 \times 10 = 53450 \)
Now, perform the division:
\( \text{R} = \frac{267250}{53450} \)
\( \text{R} = 5 \)
So, the rate of simple interest per annum is 5%.
Verification
Let's verify this rate using the original formula:
\( \text{SI} = \frac{5345 \times 5 \times 10}{100} \)
\( \text{SI} = \frac{5345 \times 50}{100} \)
\( \text{SI} = \frac{267250}{100} \)
\( \text{SI} = 2672.50 \)
This matches the given simple interest, confirming our calculated rate is correct.
Summary of Calculation
| Principal (P) | Rs. 5,345 |
| Time (T) | 10 years |
| Simple Interest (SI) | Rs. 2,672.50 |
| Formula for Rate (R) | \( R = \frac{SI \times 100}{P \times T} \) |
| Calculation | \( R = \frac{2672.50 \times 100}{5345 \times 10} = \frac{267250}{53450} \) |
| Rate (R) | 5% |
The calculated rate of simple interest per annum is 5%.
Revision Table: Simple Interest Concepts
| Term | Definition | Formula |
|---|---|---|
| Principal (P) | The initial amount of money invested or borrowed. | - |
| Simple Interest (SI) | Interest calculated only on the principal amount. | \( \frac{P \times R \times T}{100} \) |
| Rate (R) | The percentage at which interest is charged or earned per year. | \( \frac{SI \times 100}{P \times T} \) |
| Time (T) | The duration for which the money is invested or borrowed (usually in years). | - |
| Amount (A) | The total sum including principal and interest. | \( A = P + SI \) |
Additional Information: Simple vs. Compound Interest
It's important to distinguish simple interest from compound interest. In compound interest, the interest earned in each period is added to the principal for the next period's calculation. This leads to earning interest on interest, resulting in faster growth of the investment over time compared to simple interest.
- Simple Interest: Interest is constant each period (if P and R are constant).
- Compound Interest: Interest increases each period because the base (principal + accumulated interest) increases.
The question specifically mentions simple interest, so we use the formula \( \text{SI} = \frac{\text{P} \times \text{R} \times \text{T}}{100} \).
Important Questions from Simple Interest
If ₹12,800 is invested in a bank for 5 years at the rate of 9% per annum simple interest. what amount is returned by the bank?
Somu has borrowed ₹10,000 from a money lender with simple interest at a rate of 7% half yearly. How much amount will he pay to the money lender after 3 years?
Find the Simple interest on Rs. 2,400 from 20 March 2019 to 31 may 2019 at \(6{1 \over 4}\) % rate?
If the simple interest for five years is equal is 35% of the principal, that rate of interest is:
A sum fetched a simple interest of Rs. 3,040 at the rate of 8% p.a in 5 years. what is the sum?
