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
Anil lent a sum of Rs. 5,000 on simple interest for 10 years in such a way that the rate of interest is 6% per annum for the first 2 years, 8% per anmum for the next 2 years and 10% per annum beyond 4 years. How much interest (in Rs.) will he earn at the end of 10 years?
What will be the simple interest on a sum of Rs. 12000 at the rate of 15 percent per annum for three years ?
If in 13 years fixed sum doubles at simple interest, what will be the interest rate per year? (correct to two decimal places)
On simple interest a sum of Rs. 640 becomes Rs. 832 in 2 years. What will Rs. 860 become in 4 years at the same rate of simple interest?
A certain sum amounts to Rs. 81840 in 3 years and to Rs. 92400 in 5 years at x% p.a. under simple interest. If the rate of interest is becomes (x + 2)%, then in how many years will the same sum double itself?
