What annual instalment will discharge a debt of Rs. 6450 due in 4 years at 5% simple Interest ?

Options

A. Rs. 1500
B. Rs. 1835
C. Rs. 1935
D. Rs. 1950

Answer

To determine the annual installment that will discharge a debt of Rs. 6450 due in 4 years at 5% simple interest, we can follow these steps:

### Step 1: Understand the formula for the total amount in simple interest
The total amount (A) due after a certain time in the case of simple interest can be expressed as:
\[ A = N \times I + \frac{I \times R \times (N - 1) \times N}{2 \times 100} \]
Where:
- \( A \) = Total amount (Rs. 6450)
- \( N \) = Number of years (4 years)
- \( I \) = Annual installment (what we need to find)
- \( R \) = Rate of interest (5%)

### Step 2: Substitute the known values into the formula
Substituting the known values into the formula:
\[ 6450 = 4I + \frac{I \times 5 \times (4 - 1) \times 4}{2 \times 100} \]

### Step 3: Simplify the equation
Calculate the term for the interest:
- \( (4 - 1) \times 4 = 3 \times 4 = 12 \)
- So, the equation becomes:
\[ 6450 = 4I + \frac{I \times 5 \times 12}{200} \]
- Simplifying the fraction:
\[ \frac{5 \times 12}{200} = \frac{60}{200} = \frac{3}{10} \]
- Thus, the equation now looks like:
\[ 6450 = 4I + \frac{3I}{10} \]

### Step 4: Combine like terms
To combine the terms involving \( I \):
- Convert \( 4I \) into a fraction with a denominator of 10:
\[ 4I = \frac{40I}{10} \]
- Now combine:
\[ 6450 = \frac{40I}{10} + \frac{3I}{10} = \frac{43I}{10} \]

### Step 5: Solve for \( I \)
To isolate \( I \), multiply both sides by 10:
\[ 64500 = 43I \]
Now, divide both sides by 43:
\[ I = \frac{64500}{43} \]

### Step 6: Calculate the value
Perform the division:
\[ I = 1500 \]

### Conclusion
The annual installment required to discharge the debt is Rs. 1500.