The simple interest on a certain sum at the rate of `12%` per annum for 4 years is Rs 1152, If the rate of interest is increased by `2%` per annum. What will' be the amount after 5 years on the same principal ?

Options

A. Rs 4280
B. Rs 4800
C. Rs 4080
D. Rs 4480

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given information
We know that the simple interest (SI) for a certain principal (P) at a rate of 12% per annum for 4 years is Rs 1152.

### Step 2: Use the formula for Simple Interest
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 3: Substitute the known values into the formula
We can substitute the values we know into the formula:
\[ 1152 = \frac{P \times 12 \times 4}{100} \]

### Step 4: Simplify the equation
First, simplify the equation:
\[ 1152 = \frac{48P}{100} \]
Multiply both sides by 100 to eliminate the fraction:
\[ 115200 = 48P \]

### Step 5: Solve for Principal (P)
Now, divide both sides by 48:
\[ P = \frac{115200}{48} = 2400 \]
So, the principal amount is Rs 2400.

### Step 6: Calculate the new rate of interest
The new rate of interest is increased by 2%, making it:
\[ R = 12\% + 2\% = 14\% \]

### Step 7: Calculate the Simple Interest for 5 years at the new rate
Now we will calculate the simple interest for 5 years at the new rate of 14%:
\[ SI = \frac{P \times R \times T}{100} \]
Substituting the values:
\[ SI = \frac{2400 \times 14 \times 5}{100} \]

### Step 8: Simplify the calculation
Calculate the simple interest:
\[ SI = \frac{2400 \times 70}{100} = \frac{168000}{100} = 1680 \]

### Step 9: Calculate the total amount after 5 years
The total amount (A) after 5 years is given by:
\[ A = P + SI \]
Substituting the values:
\[ A = 2400 + 1680 = 4080 \]

### Step 10: Final amount
Thus, the total amount after 5 years is Rs 4080.

### Summary of the steps:
1. Understand the problem and identify the variables.
2. Use the formula for Simple Interest.
3. Substitute known values and simplify.
4. Solve for the Principal amount.
5. Calculate the new interest rate.
6. Calculate the new Simple Interest for the new rate.
7. Calculate the total amount after the specified time.