If the present worth of a certain sum due 2 yr hence at 10% per annum compound interest is 2000, find the sum.

Answer

To solve the problem of finding the sum due in 2 years at 10% per annum compound interest when the present worth is Rs. 2000, we can follow these steps:

### Step 1: Understand the formula for Present Worth (PW)
The Present Worth (PW) of a sum due in the future can be calculated using the formula:
\[ PW = \frac{S}{(1 + r)^n} \]
where:
- \( PW \) = Present Worth
- \( S \) = Future Sum (the amount we want to find)
- \( r \) = Rate of interest per annum (in decimal)
- \( n \) = Number of years

### Step 2: Substitute the known values into the formula
In this case:
- \( PW = 2000 \)
- \( r = 10\% = 0.10 \)
- \( n = 2 \)

Substituting these values into the formula gives:
\[ 2000 = \frac{S}{(1 + 0.10)^2} \]

### Step 3: Calculate \( (1 + r)^n \)
Calculate \( (1 + 0.10)^2 \):
\[ (1 + 0.10)^2 = (1.10)^2 = 1.21 \]

### Step 4: Rearrange the equation to solve for \( S \)
Now, we can rearrange the equation to find \( S \):
\[ S = PW \times (1 + r)^n \]
Substituting the values we have:
\[ S = 2000 \times 1.21 \]

### Step 5: Perform the multiplication
Now calculate:
\[ S = 2000 \times 1.21 = 2420 \]

### Final Answer
Thus, the future sum due in 2 years is:
\[ S = 2420 \]