Final answer:
Hannah's loan had a simple interest rate of 4.5% per year. This was calculated by using the simple interest formula I = PRT with the principal amount of $2000, total interest of $180, and time of 2 years.
Step-by-step explanation:
To find the simple interest rate of Hannah's loan, we can use the formula for simple interest, which is I = PRT, where I is the interest, P is the principal amount borrowed, R is the rate of interest per year, and T is the time in years. Hannah borrowed $2000 and agreed to pay back $2180 after 2 years, which means the total interest I is $180 ($2180 - $2000).
Now, we can plug in the values we know into the formula and solve for R:
I = PRT becomes $180 = $2000 * R * 2 years.
Divide both sides by $2000 * 2 to find R:
R = $180 / ($2000 * 2).
This gives us:
R = $180 / $4000 = 0.045 or 4.5% per year. Therefore, the simple interest rate of the loan was 4.5%.