A sum of Rs. 1500 amounts to Rs. 2175 in 3 years at simple interest. If rate of interest is increased by 3 percent, then what will be the new amount?
Rs. 2310
Calculating New Amount with Increased Simple Interest Rate
The problem asks us to find the new amount received after 3 years if the simple interest rate is increased by 3 percent, starting with a principal of Rs. 1500 that initially amounts to Rs. 2175 in 3 years.
Understanding the Simple Interest Calculation
Simple interest is calculated only on the initial principal amount. The formula for simple interest is:
\( I = \frac{P \times R \times T}{100} \)
Where:
- \( I \) is the Simple Interest
- \( P \) is the Principal Amount
- \( R \) is the Rate of Interest per annum
- \( T \) is the Time in years
The Amount (\( A \)) is the sum of the Principal and the Simple Interest:
\( A = P + I \)
Step-by-Step Solution to Find the New Amount
Step 1: Calculate the Simple Interest Earned Initially
Given:
- Principal (\( P \)) = Rs. 1500
- Amount (\( A \)) = Rs. 2175
- Time (\( T \)) = 3 years
The simple interest (\( I \)) earned in 3 years is the difference between the Amount and the Principal.
\( I = A - P \)
\( I = 2175 - 1500 \)
\( I = 675 \)
So, the simple interest earned in 3 years is Rs. 675.
Step 2: Find the Original Rate of Interest
We can use the simple interest formula to find the original rate (\( R \)).
\( I = \frac{P \times R \times T}{100} \)
Substitute the known values:
\( 675 = \frac{1500 \times R \times 3}{100} \)
\( 675 = \frac{4500 \times R}{100} \)
\( 675 = 45 \times R \)
Now, solve for \( R \):
\( R = \frac{675}{45} \)
Let's perform the division:
| Calculation | Result |
|---|---|
| \(675 \div 45\) | \(15\) |
So, the original rate of interest (\( R \)) is 15% per annum.
Step 3: Determine the New Rate of Interest
The problem states that the rate of interest is increased by 3 percent.
New Rate (\( R_{new} \)) = Original Rate + Increase
\( R_{new} = 15\% + 3\% \)
\( R_{new} = 18\% \)
The new rate of interest is 18% per annum.
Step 4: Calculate the New Simple Interest
Now, calculate the simple interest using the original Principal (\( P \)), the new Rate (\( R_{new} \)), and the same Time (\( T \)).
\( I_{new} = \frac{P \times R_{new} \times T}{100} \)
Substitute the values:
\( I_{new} = \frac{1500 \times 18 \times 3}{100} \)
\( I_{new} = \frac{1500}{100} \times 18 \times 3 \)
\( I_{new} = 15 \times 18 \times 3 \)
\( I_{new} = 15 \times 54 \)
Let's multiply \( 15 \times 54 \):
| Calculation | Result |
|---|---|
| \(15 \times 54\) | \(810\) |
The new simple interest (\( I_{new} \)) is Rs. 810.
Step 5: Calculate the New Amount
The new amount (\( A_{new} \)) is the sum of the Principal and the new Simple Interest.
\( A_{new} = P + I_{new} \)
\( A_{new} = 1500 + 810 \)
\( A_{new} = 2310 \)
The new amount will be Rs. 2310.
Summary of Calculations
| Item | Value | Calculation/Source |
|---|---|---|
| Principal (\(P\)) | Rs. 1500 | Given |
| Initial Amount (\(A\)) | Rs. 2175 | Given |
| Time (\(T\)) | 3 years | Given |
| Initial Simple Interest (\(I\)) | Rs. 675 | \(A - P = 2175 - 1500\) |
| Original Rate (\(R\)) | 15% | \(\frac{I \times 100}{P \times T} = \frac{675 \times 100}{1500 \times 3}\) |
| Rate Increase | 3% | Given |
| New Rate (\(R_{new}\)) | 18% | \(15\% + 3\%\) |
| New Simple Interest (\(I_{new}\)) | Rs. 810 | \(\frac{P \times R_{new} \times T}{100} = \frac{1500 \times 18 \times 3}{100}\) |
| New Amount (\(A_{new}\)) | Rs. 2310 | \(P + I_{new} = 1500 + 810\) |
The final answer is Rs. 2310.
Revision Table: Simple Interest Concepts
| Term | Definition | Formula (Simple Interest) |
|---|---|---|
| Principal (P) | The initial amount of money borrowed or invested. | N/A |
| Amount (A) | The total sum received back, including principal and interest. | \(A = P + I\) |
| Interest (I) | The extra money paid for using borrowed money or earned on investment. | \(I = A - P\) or \(I = \frac{P \times R \times T}{100}\) |
| Rate of Interest (R) | The percentage at which interest is calculated per annum. | \(R = \frac{I \times 100}{P \times T}\) |
| Time (T) | The duration for which the money is borrowed or invested, usually in years. | \(T = \frac{I \times 100}{P \times R}\) |
Additional Information: Impact of Rate Increase on Simple Interest
In simple interest, the interest earned is directly proportional to the rate of interest for a fixed principal and time. This means if the rate increases, the interest earned also increases proportionally. An increase of 3% in the rate over 3 years for a principal of Rs. 1500 leads to an additional interest of:
Additional Interest = \( \frac{P \times (\text{Increase in R}) \times T}{100} \)
Additional Interest = \( \frac{1500 \times 3 \times 3}{100} \)
Additional Interest = \( \frac{1500 \times 9}{100} \)
Additional Interest = \( 15 \times 9 \)
Additional Interest = Rs. 135
The original interest was Rs. 675. The new interest should be Rs. 675 + Rs. 135 = Rs. 810, which matches our calculation in Step 4.
The original amount was Rs. 2175. The new amount will be the original amount plus the additional interest:
New Amount = Original Amount + Additional Interest
New Amount = Rs. 2175 + Rs. 135
New Amount = Rs. 2310
This alternative calculation confirms the result and highlights how a change in rate directly impacts the simple interest and the final amount.
Important Questions from Simple Interest
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest ?
Nirav and Mehul borrowed Rs.4000 and Rs.5000 respectively for 2.5 years at the rate of x% per annum. Mehul paid Rs 125 more interest than Nirav. Find x.
If the interest on a sum of Rs.1200 is more than the interest on Rs.1000 by Rs.120 in three years, then what is the rate of interest per annum?.
The difference between the simple interest received from two banks on Rs. 500 for two years is Rs. 2.50. What is the difference between their rates?
A sum of Rs.1200 becomes Rs.1560 at a rate of simple interest in 3 years. In how many years will the sum of Rs.800 amount to Rs.1120 at the same rate of simple interest?
