Final answer:
To find the outstanding loan balance at the end of the fourth year, calculate the amount of each quarterly payment and subtract it from the original loan amount. The correct answer is A. $3407.98
Step-by-step explanation:
To find the outstanding loan balance at the end of the fourth year, we need to calculate the amount of each quarterly payment and subtract it from the original loan amount.
The loan is being repaid over 9 years, so there are 36 quarterly payments (9 years x 4 quarters). The interest rate is 5.9% convertible quarterly, which means it is applied quarterly.
First, we can calculate the quarterly interest rate by dividing the annual rate by 4: 5.9% / 4 = 1.475%
Next, we can use the formula for the present value of an ordinary annuity to find the amount of each quarterly payment:
Payment = Loan Amount / [(1 + Interest Rate)^Number of Payments - 1]
Using this formula, we can calculate the amount of each quarterly payment:
Payment = $5500 / [(1 + 1.475%)^36 - 1]
After finding the amount of each quarterly payment, we can subtract the total of the first 16 quarterly payments (4 years x 4 quarters) from the original loan amount of $5500 to find the outstanding balance at the end of the fourth year.
The correct answer is A. $3407.98