19.1 - Mortgage Math III & Real Estate Borrowing Flashcards
(21 cards)
Mortgages are subject to variety of potential fees:
underwriting fee, document processing fee, appraisal fee, origination fee, etc
What are ‘points and fees’ in the context of a mortgage?
They are upfront costs borrowers pay at closing. ‘Fees’ are one-time charges for services (e.g., underwriting, document processing, appraisal, origination), while ‘points’ are optional interest-rate buy-downs purchased for an upfront price.
nterest rate points are an opportunity
to reduce the interest rate of the
mortgage, in exchange for an upfront
charge.
– A point is 1% of the total loan
amount
List four typical mortgage fees lenders may charge.
Underwriting fee, document-processing fee, appraisal fee, origination fee.
In mortgage lending, what is a ‘point’?
One point equals 1% of the total loan amount and is paid upfront to reduce the mortgage’s interest rate.
How do interest-rate points benefit a borrower?
Paying points lowers the contract interest rate, cutting monthly payments and total interest over time—valuable if the borrower keeps the loan long enough to recoup the upfront cost.
Describe Option 1 in the slides’ example.
A $200,000, 30-year fixed-rate mortgage at 4% with $500 in standard fees and no points.
Describe Option 2 in the slides’ example.
A $200,000, 30-year fixed-rate mortgage at 3.75% plus the same $500 in fees and $2,000 for points.
What trade-off do the two options illustrate?
Higher interest rate with lower upfront cost vs. lower interest rate with higher upfront cost (points).
What is the primary goal of the Annual Percentage Rate (APR) disclosure?
To create a single rate that lets borrowers compare loans that have different upfront costs.
Conceptually, how is APR defined?
It is the discount rate (yield-to-maturity) that equates the loan amount today with the present value of all future monthly payments after accounting for upfront costs.
Name the two standard ways to compute APR shown on the slide.
- Include fees in the financed balance when calculating monthly payments, then back-solve for the rate. 2. Exclude fees from the balance, compute payments on the pure loan amount, then solve for the rate using the loan amount minus fees as the present value.
Why can a fixed-payment mortgage be treated as an annuity?
Because it is a series of equal payments; its present value equals the PV of that annuity discounted at the loan’s interest rate.
Write the formula that gives the monthly payment PMT for a loan.
PMT = PV × r/12 / (1 - (1 + r/12)^(-12n))
where PV = loan amount, r = annual interest rate, n = years.
Which Excel/Google Sheets function uses the same formula but solves for the interest rate?
RATE.
What APRs did the slides compute for Option 1 vs. Option 2?
Option 1 ≈ 4.02%, Option 2 ≈ 3.85%.
How does early repayment affect APR’s usefulness?
APR assumes the loan is held to maturity; if repaid early (sell, move, refinance) it understates the true cost, especially for loans with large upfront fees.
For which types of U.S. consumer loans must lenders disclose APR?
Mortgages, car loans, credit cards, and many other consumer credit products.
Why might APR still miss some borrower costs?
Regulations dictate which fees count; certain optional or third-party costs may be excluded, so APR can omit expenses the borrower actually pays.
What additional analysis should borrowers perform beyond comparing APRs?
Calculate the ‘break-even’ horizon: divide the upfront point cost by the monthly payment savings to see how long they must keep the loan for points to pay off.
Identify the three variables shared by the payment and APR equations.
PV (present value or loan amount), r (interest rate), and n (number of periods).
Summarize the slides’ overall message about points, fees, and APR.
Use APR to standardize loan comparisons but always account for holding period, excluded fees, and the break-even on buying points before deciding which mortgage is truly cheaper.
