The true discount on Rs. 2080 due 2 years hence is Rs. 80. Find the rate per cent-

Options

A. `4%`
B. `8%`
C. `2%`
D. None of these

Answer

To find the rate percent given the true discount on a certain amount due in the future, we can follow these steps:

### Step 1: Identify the given values
- Amount (A) = Rs. 2080
- True Discount (TD) = Rs. 80
- Time (T) = 2 years

### Step 2: Calculate the Present Worth (PW)
The Present Worth can be calculated using the formula:
\[ \text{Present Worth (PW)} = \text{Amount (A)} - \text{True Discount (TD)} \]

Substituting the values:
\[ \text{PW} = 2080 - 80 = 2000 \]

### Step 3: Use the formula for Rate (R)
The formula for the rate of interest is given by:
\[ R = \frac{100 \times \text{True Discount (TD)}}{\text{Present Worth (PW)} \times \text{Time (T)}} \]

### Step 4: Substitute the values into the formula
Substituting the known values into the formula:
\[ R = \frac{100 \times 80}{2000 \times 2} \]

### Step 5: Calculate the rate
First, calculate the denominator:
\[ 2000 \times 2 = 4000 \]

Now substitute back into the equation:
\[ R = \frac{8000}{4000} = 2 \]

### Step 6: State the final answer
Thus, the rate percent is:
\[ R = 2\% \]

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