What annual payment will discharge a debt of X 1092 due in 2 yr at 12% simple interest?

Options

A. X725
B. X325
C. X515
D. X400

Answer

To solve the problem of determining the annual payment that will discharge a debt of X 1092 due in 2 years at 12% simple interest, we can follow these steps:

### Step 1: Identify the given values
- Principal (P) = 1092
- Time (T) = 2 years
- Rate of Interest (R) = 12%

### Step 2: Use the formula for annual payment
The formula for calculating the annual payment (A) is given by:

\[ A = \frac{P}{\frac{R \cdot T}{100} + T} \]

Where:
- \( P \) is the principal amount (debt)
- \( R \) is the rate of interest
- \( T \) is the time in years

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:

\[ A = \frac{1092}{\frac{12 \cdot 2}{100} + 2} \]

### Step 4: Calculate the interest part
Calculate the interest part:

\[ \frac{12 \cdot 2}{100} = \frac{24}{100} = 0.24 \]

Now add this to the time:

\[ 0.24 + 2 = 2.24 \]

### Step 5: Calculate the annual payment
Now substitute this back into the formula for A:

\[ A = \frac{1092}{2.24} \]

### Step 6: Perform the division
Now, perform the division:

\[ A = 488.39 \]

### Step 7: Round to the nearest whole number
Since we typically deal with whole currency amounts, we round this to:

\[ A \approx 488 \]

### Final Answer
Thus, the annual payment that will discharge the debt is approximately **X 488**.

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