A person deposited Rs. 500 for 3 years, Rs. 650 for 5 years, and Rs. 1,250 for 7 years. He received a total simple interest of Rs. 1,620. The rate of interest per annum is:
12%
Understanding the Simple Interest Problem
The question asks us to find the annual rate of simple interest given that a person made three different deposits for different time periods and received a total simple interest amount.
Here's the information provided:
- Deposit 1: Principal (P1) = Rs. 500, Time (T1) = 3 years
- Deposit 2: Principal (P2) = Rs. 650, Time (T2) = 5 years
- Deposit 3: Principal (P3) = Rs. 1,250, Time (T3) = 7 years
- Total Simple Interest (SITotal) = Rs. 1,620
We need to find the rate of interest (R), which is assumed to be the same for all deposits and constant per annum.
Calculating the Simple Interest Rate
The formula for simple interest (SI) is:
\(SI = \frac{P \times R \times T}{100}\)
Where:
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum (in percentage)
- \(T\) = Time period in years
The total simple interest received is the sum of the simple interests from each individual deposit.
\(SI_{Total} = SI_1 + SI_2 + SI_3\)
Let R be the rate of interest per annum. We can write the equation as:
\(1620 = \frac{P_1 \times R \times T_1}{100} + \frac{P_2 \times R \times T_2}{100} + \frac{P_3 \times R \times T_3}{100}\)
Substitute the given values into the equation:
\(1620 = \frac{500 \times R \times 3}{100} + \frac{650 \times R \times 5}{100} + \frac{1250 \times R \times 7}{100}\)
Now, let's simplify each term:
- \(\frac{500 \times R \times 3}{100} = \frac{1500 \times R}{100} = 15R\)
- \(\frac{650 \times R \times 5}{100} = \frac{3250 \times R}{100} = 32.5R\)
- \(\frac{1250 \times R \times 7}{100} = \frac{8750 \times R}{100} = 87.5R\)
So, the equation becomes:
\(1620 = 15R + 32.5R + 87.5R\)
Combine the terms with R:
\(1620 = (15 + 32.5 + 87.5)R\)
\(1620 = 135R\)
Now, solve for R:
\(R = \frac{1620}{135}\)
Let's perform the division:
\(R = 12\)
The rate of interest per annum is 12%.
Let's verify the result:
- SI for 500 at 12% for 3 years: \(\frac{500 \times 12 \times 3}{100} = \frac{18000}{100} = 180\)
- SI for 650 at 12% for 5 years: \(\frac{650 \times 12 \times 5}{100} = \frac{39000}{100} = 390\)
- SI for 1250 at 12% for 7 years: \(\frac{1250 \times 12 \times 7}{100} = \frac{105000}{100} = 1050\)
Total Simple Interest = \(180 + 390 + 1050 = 1620\)
This matches the given total simple interest, confirming our calculated rate is correct.
| Deposit | Principal (P) | Time (T) | Simple Interest (SI) at 12% |
|---|---|---|---|
| 1 | Rs. 500 | 3 years | \(\frac{500 \times 12 \times 3}{100} = 180\) |
| 2 | Rs. 650 | 5 years | \(\frac{650 \times 12 \times 5}{100} = 390\) |
| 3 | Rs. 1,250 | 7 years | \(\frac{1250 \times 12 \times 7}{100} = 1050\) |
| Total Simple Interest | \(180 + 390 + 1050 = 1620\) | ||
The calculated rate of interest matches the provided information.
Revision Table: Simple Interest Concepts
| Term | Definition | Formula (for Simple Interest) |
|---|---|---|
| Principal (P) | The initial amount of money deposited or borrowed. | N/A |
| Rate (R) | The percentage at which interest is charged or earned per period (usually per annum). | N/A |
| Time (T) | The duration for which the money is deposited or borrowed. | N/A |
| Simple Interest (SI) | Interest calculated only on the principal amount. | \(SI = \frac{P \times R \times T}{100}\) |
| Amount (A) | The total sum of the principal and the interest earned. | \(A = P + SI\) or \(A = P(1 + \frac{RT}{100})\) |
Additional Information on Simple Interest
Simple interest is a basic and common method for calculating interest on a principal amount. Unlike compound interest, simple interest does not add the earned interest back to the principal to calculate future interest. This means that the interest earned each period remains constant, assuming the principal and rate are fixed.
Key characteristics of simple interest:
- Calculated only on the original principal.
- The amount of interest earned per period is fixed.
- Easier to calculate compared to compound interest.
- Often used for short-term loans or simple deposit schemes.
In this problem, the total simple interest is the sum of simple interests calculated independently for each principal and time period using the same rate. This highlights how simple interest from different investments simply adds up.
Similar Questions
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Important Questions from Simple Interest
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