Find the sum due, if the true discount on a sum due 2 yr hence at 7% be X672.

Options

A. X 5500
B. X 5425
C. X 5472
D. X 5300

Answer

To solve the problem, we need to find the sum due given the true discount (TD) and the interest rate over a specified time period. Here’s a step-by-step solution:

### Step 1: Understand the given information
- True Discount (TD) = X672
- Rate (r) = 7%
- Time (t) = 2 years

### Step 2: Use the formula for Present Worth (PW)
The formula for Present Worth (PW) in terms of True Discount is:
\[ PW = \frac{100 \times TD}{r \times t} \]
Where:
- TD = True Discount
- r = Rate of interest (in percentage)
- t = Time (in years)

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ PW = \frac{100 \times 672}{7 \times 2} \]

### Step 4: Calculate the denominator
Calculate \(7 \times 2\):
\[ 7 \times 2 = 14 \]

### Step 5: Substitute back into the formula
Now substitute back into the formula:
\[ PW = \frac{100 \times 672}{14} \]

### Step 6: Calculate the numerator
Calculate \(100 \times 672\):
\[ 100 \times 672 = 67200 \]

### Step 7: Divide to find Present Worth
Now divide \(67200\) by \(14\):
\[ PW = \frac{67200}{14} = 4800 \]

### Step 8: Calculate the Sum Due (S)
Now that we have the Present Worth, we can find the Sum Due (S) using the formula:
\[ S = PW + TD \]
Substituting the values we have:
\[ S = 4800 + 672 \]

### Step 9: Add to find the final sum
Now add \(4800\) and \(672\):
\[ S = 4800 + 672 = 5472 \]

### Final Answer
The sum due is X5472.

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