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

Answer Details

Simple interest is a way to calculate the interest earned or paid only on the original principal amount over a period of time. The formula for simple interest is:

\[ I = P \times r \times t \] where:
\( I \) = Interest earned
\( P \) = Principal (initial amount invested or saved)
\( r \) = Rate of interest per year (as a decimal)
\( t \) = Time in years

But in this question, the amount realized (final amount) after saving for a certain period is given. The formula linking the final amount (\( A \)) with the principal and the simple interest is:

\[ A = P + I \]

Substitute the formula for simple interest into this:

\[ A = P + (P \times r \times t) \] \[ A = P(1 + r \times t) \]

We are told:

• \( A = 600,\!000 \)
• \( r = 5\% = 0.05 \)
• \( t = 4 \) years

Let \( P = y \), the original principal. We plug in the values:

\[ 600,\!000 = y(1 + 0.05 \times 4) \] \[ 600,\!000 = y(1 + 0.20) \] \[ 600,\!000 = y \times 1.20 \]

To get the principal, divide both sides by 1.20:

\[ y = \frac{600,\!000}{1.20} \] \[ y = 500,\!000 \]

The correct principal (\( y \)) is # 500,000. This means that if #500,000 was saved at 5% simple interest for 4 years, the total amount after 4 years would become #600,000.

Why this works: Simple interest adds a fixed percentage of the principal for each year. In this case, 5% of 500,000 is 25,000 per year, and over 4 years that's 100,000. Adding that to the original 500,000 gives a total of 600,000.