Josie borrows 2000 and repays a final amount of 2186.17 in 2 years. What annual pre-of interest, compounded semi-annually, is she being offered on this loan? A) 4% B) 3% C) 4.5% D) 3.5% Question 3(1 point)

## Step 1: Convert the annual interest rate to a semi-annual rate.### Let be the annual interest rate. Since the interest is compounded semi-annually, the semi-annual interest rate is .## Step 2: Calculate the number of compounding periods.### The loan is for 2 years, and the interest is compounded semi-annually (twice a year). Therefore, the number of compounding periods is .## Step 3: Set up the compound interest formula.### The formula for compound interest is , where is the final amount, is the principal, is the annual interest rate, is the number of times interest is compounded per year, and is the time in years. In this case, 2186.17 P = \ , , and . We need to solve for . So, .## Step 4: Solve for the annual interest rate.### Simplify the equation: .### Divide both sides by 2000: .### ### Take the fourth root of both sides: .### ### Subtract 1 from both sides: ### Multiply both sides by 2: ### Convert to percentage: