What will be the present worth of 4840 due 2 yr hence, when the interest is compounded at 10% per annum? Also, find true discount.

Answer

To solve the problem of finding the present worth of ₹4840 due in 2 years at an interest rate of 10% per annum compounded annually, and to find the true discount, we can follow these steps:

### Step 1: Understand the formula for Present Worth (PW)
The formula for Present Worth when the amount is compounded is given by:
\[ PW = \frac{A}{(1 + r)^n} \]
where:
- \( A \) = Future Amount (₹4840)
- \( r \) = Rate of interest (10% or 0.10)
- \( n \) = Number of years (2)

### Step 2: Substitute the values into the formula
Substituting the values into the formula:
\[ PW = \frac{4840}{(1 + 0.10)^2} \]
\[ PW = \frac{4840}{(1.10)^2} \]
\[ PW = \frac{4840}{1.21} \]

### Step 3: Calculate the denominator
Calculating \( (1.10)^2 \):
\[ (1.10)^2 = 1.21 \]

### Step 4: Calculate Present Worth
Now, calculate the Present Worth:
\[ PW = \frac{4840}{1.21} \approx 4000 \]

### Step 5: Find the True Discount
True Discount (TD) is calculated as:
\[ TD = A - PW \]
Substituting the values:
\[ TD = 4840 - 4000 \]
\[ TD = 840 \]

### Final Answers
- Present Worth = ₹4000
- True Discount = ₹840

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