If Rs. 72 amounts to Rs. 104.4 in 3 years, what will Rs. 120 amount to in 5 years at the same rate percent per annum?
Rs. 210
Understanding Simple Interest Calculations
This question involves calculating simple interest and finding the final amount based on given principal, rate, and time. We are given the details of one investment to determine the rate of interest and then use that rate to find the final amount for a different investment.
Step-by-Step Solution to Find the Rate
In the first part of the question, we are given:
- Principal (P) = Rs. 72
- Amount (A) = Rs. 104.4
- Time (T) = 3 years
The simple interest (SI) earned is the difference between the Amount and the Principal.
Simple Interest (SI) = Amount - Principal
\( \text{SI} = 104.4 - 72 \)
\( \text{SI} = 32.4 \) Rupees
Now we use the formula for simple interest to find the rate (R) per annum:
\( \text{SI} = \frac{P \times R \times T}{100} \)
Substitute the known values:
\( 32.4 = \frac{72 \times R \times 3}{100} \)
To solve for R, we can rearrange the formula:
\( 32.4 \times 100 = 72 \times 3 \times R \)
\( 3240 = 216 \times R \)
\( R = \frac{3240}{216} \)
\( R = 15 \)
So, the rate of interest is 15% per annum.
Calculating the Amount for the Second Investment
Now we use the rate (R = 15%) calculated in the first part for the second investment:
- Principal (P') = Rs. 120
- Time (T') = 5 years
- Rate (R) = 15% per annum
First, calculate the simple interest (SI') for this investment using the same formula:
\( \text{SI}' = \frac{P' \times R \times T'}{100} \)
Substitute the values:
\( \text{SI}' = \frac{120 \times 15 \times 5}{100} \)
\( \text{SI}' = \frac{120 \times 75}{100} \)
\( \text{SI}' = \frac{9000}{100} \)
\( \text{SI}' = 90 \) Rupees
The amount (A') for the second investment is the sum of the Principal and the Simple Interest:
\( \text{Amount} = \text{Principal} + \text{Simple Interest} \)
\( \text{A}' = \text{P}' + \text{SI}' \)
\( \text{A}' = 120 + 90 \)
\( \text{A}' = 210 \)
So, Rs. 120 will amount to Rs. 210 in 5 years at the same rate of 15% per annum.
Summary of Calculations
| Case | Principal | Amount | Time (Years) | Simple Interest | Rate (% p.a.) |
|---|---|---|---|---|---|
| 1 | Rs. 72 | Rs. 104.4 | 3 | Rs. \(104.4 - 72 = 32.4\) | \( \frac{32.4 \times 100}{72 \times 3} = 15 \) |
| 2 | Rs. 120 | Rs. 210 (Calculated) | 5 | \( \frac{120 \times 15 \times 5}{100} = 90 \) | 15 |
The final amount for the second investment is Rs. 210.
Revision Table: Key Simple Interest Concepts
| Term | Definition | Formula |
|---|---|---|
| Principal (P) | The initial amount of money invested or borrowed. | N/A |
| Amount (A) | The total sum at the end of the investment period, including principal and interest. | \( A = P + \text{SI} \) |
| Simple Interest (SI) | Interest calculated only on the principal amount. | \( \text{SI} = \frac{P \times R \times T}{100} \) |
| Rate of Interest (R) | The percentage at which interest is calculated annually on the principal. | \( R = \frac{\text{SI} \times 100}{P \times T} \) |
| Time (T) | The duration for which the money is invested or borrowed, usually in years. | N/A |
Additional Information on Simple Interest
Simple interest is a basic concept in finance. It is the easiest way to calculate interest on a loan or investment because it is only based on the original principal amount. Unlike compound interest, simple interest does not earn interest on previously accumulated interest.
Key points about simple interest:
- It is calculated using the principal amount only.
- The interest amount is constant for each period (assuming the rate and principal remain unchanged).
- It is often used for short-term loans or simple investments.
- Understanding simple interest is crucial before learning about more complex concepts like compound interest or annuities.
Similar Questions
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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?
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