Final answer:
Anna has the option to finance her $1500 appliance for 2 years at a 6% simple interest rate or 2 years at 5.5% compounded continuously. The total repayment amount for the simple interest option is approximately $795, while the total repayment amount for the continuous compounding option is approximately $1592.46.
Step-by-step explanation:
Anna is planning to purchase a $1500 appliance and is considering two financing options. Option 1 is to finance it for 2 years at a 6% simple interest rate. Option 2 is to finance it for 2 years at 5.5% compounded continuously.
Option 1: Simple Interest
- Find the interest amount: $1500 * 0.06 = $90
- Find the total amount to repay: $1500 + $90 = $1590
- Divide the total by the number of years: $1590 / 2 = $795
Option 2: Continuous Compounding
- Use the formula A = P*e^(rt), where A is the final amount, P is the initial amount, e is Euler's number, r is the interest rate, and t is the time in years.
- For the continuous compounding option: A = $1500 * e^(0.055*2) ≈ $1592.46
Therefore, Anna would need to repay around $795 for the simple interest option and around $1592.46 for the continuous compounding option.