Final answer:
The annual effective interest rate for the loan with a 2% monthly interest compounded yearly is 2%. To find the yearly loan payment, use the present value of an annuity formula considering the loan amount, interest rate, and three-year term. The details of the payment schedule can be calculated using a financial calculator or Excel.
Step-by-step explanation:
Calculating the Annual Effective Interest Rate and Loan Payment
To calculate the annual effective interest rate for a 2% per month compounded yearly, you would use the following formula for effective interest rate (EIR): EIR = (1 + i)n - 1, where i is the monthly interest rate and n is the number of compounding periods per year. Since the interest rate is compounded yearly, there is one compounding period per year (n=1). Thus, the EIR would be (1 + 0.02)1 - 1 = 0.02 or 2%.
To calculate the yearly loan payment, you would use the formula for the present value of an annuity, which is based on the loan amount, the interest rate, and the number of payment periods. The loan repayment schedule would be created based on these factors to determine the equal payments that would be made to pay off the loan over three years. A financial calculator or a software program like Excel could be used to calculate these payments accurately.
In contrast, simple interest calculations, like in question 6 and 7 provided in the examples, use a different approach where interest is not compounded, and the formula for total simple interest is I = P x r x t, where P is the principal, r is the interest rate, and t is the time in years.