Question

write an equation to find the amount of simple interest, a, earned on a $600 investment after 1\frac{1}{2} years if the semi-annual (6-month) interest rate is 2%.

Explanation:

Step1: Recall simple interest formula

The formula for simple interest is \( A = P \times r \times t \), where \( P \) is the principal amount, \( r \) is the interest rate per period, and \( t \) is the number of periods.

Step2: Identify values of \( P \), \( r \), and \( t \)

• Principal \( P=\$600 \).
• The semi - annual interest rate \( r = 2\%=0.02 \).
• The time period: \( 1\frac{1}{2}\) years. Since the interest is compounded semi - annually (every 6 months), the number of 6 - month periods in \( 1\frac{1}{2}=\frac{3}{2}\) years is \( t=\frac{3}{2}\div\frac{1}{2}=3 \) (because each year has 2 six - month periods, so \( 1.5\times2 = 3\) periods).

Step3: Substitute values into the formula

Substitute \( P = 600 \), \( r=0.02 \) and \( t = 3 \) into the simple interest formula \( A=P\times r\times t \). We get \( A=600\times0.02\times3 \).

Answer:

The equation to find the amount of simple interest \( A \) is \( A = 600\times0.02\times3 \) (or \( A=Prt \) with \( P = 600 \), \( r = 0.02 \), \( t = 3 \))