Final answer:
The borrower must assess the incremental cost of borrowing when choosing between two loan options offered by the lender: borrowing 80% of the property's value at 5.5% or 90% at 6.5%. Considering their $100,000 in savings, the borrower will evaluate the total cost over 30 years to see how the higher loan amount at a higher interest rate compares to borrowing less with a higher down payment.
Step-by-step explanation:
If a property sells for $500,000 and a lender offers two borrowing options, the borrower needs to determine the incremental cost of borrowing. The first option is to lend 80% at a nominal rate of 5.5%, and the second option is to lend 90% at a rate of 6.5%, both loans maturing in 30 years with monthly payments. For the first option, the loan amount would be 80% of $500,000, which is $400,000. At a 5.5% nominal rate, monthly payments would be calculated based on that rate and term. On the other hand, the second option would entail a loan amount of 90% of $500,000, which is $450,000, but at a higher interest rate of 6.5%. The borrower will have to compare the monthly payments for both options to understand the incremental cost involved with borrowing an additional 10% of the property value. Assuming the borrower has $100,000 in savings, they could potentially choose to make a larger down payment with the first loan option and thus borrow less, leading to a potentially lower total cost over the life of the loan despite the lower interest rate. In essence, the incremental cost of borrowing helps the borrower understand how much more they will pay in total for borrowing additional funds at a higher interest rate.