What equal installment of annual payment will discharge debit is due as Rs 848 at the end of 4 years at 4% per annum simple interest.

Options

A. Rs 250
B. Rs 200
C. Rs 150
D. Rs 350

Answer

To solve the problem of finding the equal installment of annual payment that will discharge a debt of Rs 848 at the end of 4 years at 4% per annum simple interest, we can follow these steps:

### Step 1: Understand the formula for equal annual installments
The formula to calculate the equal annual installment (A) is given by:

\[ A = \frac{P \times r \times t}{100 \times t + \frac{t(t-1) \times r}{2}} \]

Where:
- \( P \) = Principal amount (the debt amount)
- \( r \) = Rate of interest (in percentage)
- \( t \) = Time period (in years)

### Step 2: Identify the values
From the question:
- \( P = 848 \)
- \( r = 4\% \)
- \( t = 4 \) years

### Step 3: Substitute the values into the formula
Now, substituting the values into the formula:

\[ A = \frac{848 \times 4 \times 4}{100 \times 4 + \frac{4(4-1) \times 4}{2}} \]

### Step 4: Calculate the denominator
First, calculate the denominator:

1. Calculate \( 100 \times t \):
\[ 100 \times 4 = 400 \]

2. Calculate \( \frac{t(t-1) \times r}{2} \):
\[ \frac{4(4-1) \times 4}{2} = \frac{4 \times 3 \times 4}{2} = \frac{48}{2} = 24 \]

3. Now, add these two results together:
\[ 400 + 24 = 424 \]

### Step 5: Calculate the numerator
Now calculate the numerator:

\[ 848 \times 4 \times 4 = 848 \times 16 = 13568 \]

### Step 6: Calculate the equal installment (A)
Now substitute the numerator and denominator back into the formula:

\[ A = \frac{13568}{424} \]

Now, perform the division:

\[ A = 32 \]

### Conclusion
The equal installment of annual payment that will discharge the debt of Rs 848 at the end of 4 years at 4% per annum simple interest is Rs 32.

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