How would you calculate the effective borrowing cost on a loan where the borrower makes a monthly payment of $899.33, assuming no prepayment?

To determine the effective borrowing cost on a loan where the borrower makes a fixed monthly payment, you can use the loan payment formula, which accounts for the principal, interest rate, and the duration of the loan. The monthly payment amount and the total loan amount allow you to find the interest rate that makes the present value of all future payments equal to the loan amount—this is effectively calculating the internal rate of return (IRR) of the cash flows associated with the loan.

In this specific case, the monthly payment is given as $899.33. To find the effective annual borrowing cost, you'd set up the equation related to the annuity due to the monthly payment, and then utilize iterative methods or a financial calculator to solve for the interest rate. This is because, in typical scenarios, the monthly payment does not directly allow for easy calculation of the interest rate without some algebraic or computational assistance.

If the calculations yield an effective annual interest rate around 6.35%, this indicates that if you were to borrow the amount represented by this monthly payment over the length of the loan, the actual cost of borrowing (accounting for the time value of money and consistent payment structure) is aligned with this interest rate.

The effective borrowing cost plays a