Answer:
[tex]3\%[/tex] p.a.
Step-by-step explanation:
The formula for simple interest is [tex]I=PRT[/tex] ([tex]I =[/tex] interest, [tex]P =[/tex] principal, [tex]R =[/tex] rate)
First, let's express the interest earned in one and three years:
[tex]I_{1} = PRT_{1}[/tex] (finding the interest earnt in one year)
[tex]I_{1} = \$ 500\times R \times 1[/tex]
[tex]=\$ 500R[/tex]
[tex]I_{2} = PRT_{2}[/tex] (finding the interest earnt in three years)
[tex]I_2 = \$ 500 \times R \times 3[/tex]
[tex]=\$ 1500R[/tex]
From the information "The difference between the total interest earned after 3 years and the total interest earned after 1 year is $30", we can write:
[tex]I_{2}-I_{1} = \$ 30[/tex]
[tex]\$ 1500R - \$500 R = \$ 30[/tex]
[tex]\$ 1000R = \$ 30[/tex]
[tex]R = 0.03[/tex]
[tex]=3\%[/tex] p.a.
∴ The annual interest rate is [tex]3\%[/tex]
Hope this helps :)
