An amount of # 600,000.00 was realized when a principal y was saved for 5% simple interest for 4 years, find the value of y

1. Analyze the question

We are given:

• Amount ($A$): # 600,000.00 (This is the total sum of the principal and the interest).
• Rate ($R$): 5% per annum.
• Time ($T$): 4 years.
• Principal ($P$): $y$ (This is what we need to find).

2. Explain the concept

In simple interest, the total amount ($A$) is the sum of the principal ($P$) and the simple interest ($I$). The formulas are:

• $I = \frac{P \times R \times T}{100}$
• $A = P + I$

By substituting the interest formula into the amount formula, we get: $A = P + \frac{P \times R \times T}{100}$ $A = P(1 + \frac{RT}{100})$

3. Show the solution

Given: $A = 600,000$ $R = 5$ $T = 4$ $P = y$

Substitute these values into the formula: $600,000 = y(1 + \frac{5 \times 4}{100})$

Simplify the expression inside the bracket: $600,000 = y(1 + \frac{20}{100})$ $600,000 = y(1 + 0.2)$ $600,000 = y(1.2)$

Now, solve for $y$: $y = \frac{600,000}{1.2}$

To make the division easier, multiply both numerator and denominator by 10: $y = \frac{6,000,000}{12}$ $y = 500,000$

4. Identify the answer

The value of $y$ is # 500,000. This corresponds to option B.

5. Tip

When dealing with simple interest problems, always remember that the "Amount" is the Principal + Interest. A common mistake students make is calculating the interest and forgetting to add it back to the principal, or confusing "Amount" with "Interest." Always check if the question asks for the interest earned or the total amount.