Julian is a student relying on student loans.He feels he would like to borrow an extra $4000 each year for the next four years to take vacations to recover from studying.Assume that no interest accrues until he completes his education and begins paying off the loan.The interest rate for the loan amount will be seven percent per year compounded monthly and he will pay it off over five years by making end of month payments.What would his monthly payment be on this loan?
A)$374
B)$267
C)$271
D)$316

Question

Quizplus · Accepted Answer

To calculate the monthly payment for Julian's loan, we first need to determine the total loan amount he will borrow over the four years, which is $4000 per year for four years, totaling $16,000. Since the interest does not accrue until he begins repayment and the interest rate is 7% per year compounded monthly, we use the formula for calculating the monthly payment on an amortizing loan, which is P = [rPV] / [1 - (1 + r)^-n], where P is the monthly payment, r is the monthly interest rate (annual rate/12), PV is the present value of the loan (total loan amount), and n is the total number of payments (months).Given:- Total loan amount (PV) = $16,000- Annual interest rate = 7% or 0.07- Monthly interest rate (r) = 0.07 / 12 = 0.00583333- Total number of payments (n) = 5 years * 12 months/year = 60 monthsPlugging these values into the formula gives us:P = [0.00583333 * 16000] / [1 - (1 + 0.00583333)^-60] = [93.33328] / [1 - (1 + 0.00583333)^-60] ≈ $316Therefore, Julian's monthly payment on this loan would be approximately $316.

Julian Is a Student Relying on Student Loans