Find the true discount of Rs 5800 due for 2 year hence the rate of interest is 8%.

Options

A. Rs 750
B. Rs 900
C. Rs 800
D. Rs 850

Answer

To find the true discount of Rs 5800 due for 2 years at a rate of interest of 8%, we can follow these steps:

### Step 1: Understand the Concept of True Discount
True discount is the difference between the present value (PV) of a sum due in the future and the future value (FV) itself. It can also be calculated using the formula:
\[ \text{True Discount} = \text{Future Value} - \text{Present Value} \]

### Step 2: Calculate the Present Value (PV)
The present value can be calculated using the formula:
\[ PV = \frac{FV}{(1 + r)^n} \]
where:
- \( FV = 5800 \) (the future value)
- \( r = \frac{8}{100} = 0.08 \) (the rate of interest)
- \( n = 2 \) (the number of years)

Substituting the values:
\[ PV = \frac{5800}{(1 + 0.08)^2} \]
\[ PV = \frac{5800}{(1.08)^2} \]
\[ PV = \frac{5800}{1.1664} \]
\[ PV \approx 4971.56 \]

### Step 3: Calculate the True Discount
Now that we have the present value, we can calculate the true discount:
\[ \text{True Discount} = FV - PV \]
\[ \text{True Discount} = 5800 - 4971.56 \]
\[ \text{True Discount} \approx 828.44 \]

### Step 4: Round Off the True Discount
Since the options provided are in whole numbers, we can round off the true discount to the nearest whole number:
\[ \text{True Discount} \approx 828 \]

### Step 5: Choose the Closest Option
Among the options provided (750, 900, 800, 850), the closest value to 828 is 800.

### Final Answer
The true discount of Rs 5800 due for 2 years at a rate of interest of 8% is approximately Rs 800.

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