Final answer:
The simple interest rate for Luke's savings account is found using the simple interest formula. With the total interest of $960 earned over 5 years on a principal of $4800, the rate is calculated as 4%.
Step-by-step explanation:
To find the simple interest rate for Luke's savings account, we use the simple interest formula: Interest (I) = Principal (P) × Rate (R) × Time (T). Luke earns $16 each month for 60 months, so the total interest he earns is $16 × 60 = $960. The principal (P) is the initial amount he puts into the savings account, which is $4800. The time (T) is in years, so 60 months is equivalent to 5 years.
We rearrange the simple interest formula to solve for the interest rate (R). The formula becomes: R = I / (P × T). Plug in the values: R = $960 / ($4800 × 5). Simplifying this gives us: R = $960 / $24000, which equals 0.04, or 4% when expressed as a percentage. Therefore, the simple interest rate for Luke's savings account is 4%.
From the given information, we can calculate the interest earned by Luke as follows:
I = $4800 · r · 60 = $16 · 60
Solving for r, we have:
r = $16 · 60 / $4800 = 0.2
The interest rate for Luke's savings account is 0.2 or 20% per year.