The problem states that an amount of $550,000$ was realized when a principal amount $x$ was saved at $2\%$ simple interest for $5$ years. We need to find the value of $x$.

1. Problem Description

The problem states that an amount of $550,000$ was realized when a principal amount $x$ was saved at $2\%$ simple interest for $5$ years. We need to find the value of $x$.

2. Solution Steps

The formula for simple interest is given by:

$Simple Interest = (Principal \times Rate \times Time) / 100$

$SI = (P \times R \times T)/100$

The amount realized is the sum of the principal and the simple interest. Therefore:

$Amount = Principal + Simple Interest$

$Amount = P + SI$

In this case, the amount is $550,000$, the principal is $x$, the rate is $2\%$, and the time is $5$ years.

We can write the equation as:

$550000 = x + (x \times 2 \times 5) / 100$

$550000 = x + (10x) / 100$

$550000 = x + x / 10$

$550000 = (10x + x) / 10$

$550000 = 11x / 10$

$5500000 = 11x$

$x = 5500000 / 11$

$x = 500000$

3. Final Answer

The value of x is $500,000$. Therefore, the answer is D. ¥500,000.00.