Chapter 4 — Exercises

Thirty-eight problems. Items marked † have worked solutions in Appendix: Answers to Selected Exercises. Use a calculator or spreadsheet for the payment formula; show your setup either way.

Unless stated otherwise, use the Linden Street facts: \$385,000 purchase, \$365,750 loan at 6.625% for 360 months, P&I \$2,341.94, taxes \$385.00, insurance \$130.00, MI \$176.78, income \$10,500.00, other debts \$1,446.00.

A. The payment

4.1 Write the payment formula and define each symbol. State the two unit errors that cause most wrong answers.

4.2 † Compute the monthly P&I on \$412,000 at 7.375% for 360 months. Show all four steps.

4.3 Compute the monthly P&I on \$412,000 at 7.375% for 180 months. State the payment increase and the total-interest saving against 4.2.

4.4 † A borrower asks you to "run it at 40 years." On the Linden Street loan, compute the payment and state, in one sentence a borrower would understand, what the ten extra years buy and cost.

4.5 Compute one month's interest on \$289,400 at 5.875%. Then estimate the full P&I payment using only the rule in §4.10 (real payment ≈ 15–20% above interest-only) and check your estimate.

4.6 † Using the per-\$1,000 factors in §4.10, estimate the P&I on a \$247,000 loan at 7.000%. Then compute it exactly and state the error in dollars.

B. Amortization

4.7 † Build the first four rows of the amortization schedule for \$200,000 at 6.000%, 360 months. Use the one-line rule and round interest to the cent each month.

4.8 Using your schedule from 4.7, state what fraction of the first payment goes to principal. Then explain, in two sentences, why that fraction rises every month without the borrower paying more.

4.9 † On the Linden Street loan, the balance after 60 payments is \$342,870.17. Compute total payments made, total principal paid, and total interest paid over those five years.

4.10 §4.2 says the schedule overshoots zero by \$3.07 at month 360 and the final payment is adjusted. Explain why the overshoot exists, and state which direction it goes and why.

4.11 † A borrower adds \$200 a month to their Linden Street payment starting with payment 1. Without building the full schedule, explain what happens to (a) the interest portion of payment 2, (b) the payoff date, and (c) the total interest. Then state the one piece of information you would need to compute the payoff date exactly.

C. PITI

4.12 Assemble PITI for: loan \$298,000 at 6.875%; taxes \$3,900/yr; insurance \$1,740/yr; HOA \$185/mo; MI factor 0.42%.

4.13 † A loan officer tells a borrower "your payment is \$2,341.94." State the two ways this goes wrong, and write the sentence they should have said instead.

4.14 Name the four traps in PITI from §4.3. For each, describe a borrower who gets hurt by it.

4.15 † A property's current tax bill is \$2,100 because the seller has owned it for nineteen years. The purchase price is \$385,000 and the local rate is approximately 1.2% of assessed value, with reassessment on transfer. Compute the tax figure you should qualify the borrower on, the monthly difference from the seller's figure, and what that difference does to the housing ratio at \$10,500 income.

D. LTV

4.16 Compute LTV: loan \$332,500, price \$350,000, appraised value \$358,000.

4.17 † Same loan and price, but the appraisal comes in at \$341,000. Compute the LTV the lender will use, the maximum 95% loan, the new required down payment, and the gap.

4.18 State the rule for which value LTV uses on a purchase. Then state what governs on a refinance.

4.19 † A borrower has a first mortgage of \$240,000 and a home equity line with a \$75,000 limit and a \$12,000 balance. The home is worth \$400,000. Compute LTV, CLTV, and HCLTV.

4.20 Explain, to a borrower, why HCLTV uses the full credit line rather than the balance.

4.21 † On the Linden Street loan, state the payment number at which the borrower may request mortgage insurance cancellation and the payment number at which it terminates automatically. State the value each is measured against, and name the statute.

E. The ratios

4.22 Compute both qualifying ratios for: PITI \$2,880; other debts \$1,120; gross monthly income \$9,400.

4.23 † A borrower has \$11,200 gross monthly income, a proposed PITI of \$3,410, an auto loan of \$610 with **8 payments remaining**, a student loan of \$295, and credit card minimums of \$180. Compute the back-end ratio both with and without the auto loan, and state which figure the underwriter will use and why.

4.24 For each of the following, state whether it counts in the back-end ratio: a 401(k) loan repayment; childcare; a co-signed auto loan the borrower's brother pays; health insurance deducted from payroll; alimony paid; the full PITI on a rental property; utilities.

4.25 † A colleague says "they're declined, they're at 46 percent." Write the three questions you would ask before accepting that conclusion.

F. What DTI cannot tell you

4.26 † Compute payment shock for the Linden Street borrowers. Then compute it for a borrower moving from \$2,650 rent to a \$2,900 PITI, and comment on which of the two files you would worry about more and why.

4.27 Construct two borrowers with identical \$10,500 gross incomes, identical debts, and identical proposed PITI — and therefore identical ratios — whose actual financial positions are very different. Name at least three differences.

4.28 §4.6 says DTI "declines people who can obviously afford it." Describe such a borrower in detail, then describe what, if anything, you could do for them. (You may reference Chapters 13, 15, and 33 speculatively.)

4.29 † A borrower qualifies at \$460,000 and is looking at \$385,000. Write the script from §4.6 in your own words. It must (a) confirm the qualification, (b) give both payment figures, and (c) let the borrower decide.

G. Points, APR, and per-diem

4.30 Using the §4.7 grid, state the cost or credit and the payment for 6.875% and for 6.500%. Then compute the break-even for buying down from par to 6.500%.

4.31 † A borrower can pay \$3,400 for one point and save \$54 a month. Compute the break-even in months and years. Then state the one question you must ask, and describe two circumstances that would make the purchase a mistake even if the borrower answers it favorably.

4.32 A lender offers 7.000% with a \$2,743.12 credit. Describe a borrower for whom that is the correct structure, and one for whom it is not.

4.33 † List which of the following are prepaid finance charges and which are excluded: origination charge, appraisal, discount points, title insurance, prepaid interest, credit report, tax service fee, recording fees, settlement fee, mortgage insurance.

4.34 The Linden Street note rate is 6.625% and the APR is 7.253%. Explain the gap to a borrower in under 80 words, and end by telling them how to use the APR against a competitor.

4.35 † State two things APR does badly. For each, describe a borrower who would be misled.

4.36 Compute per-diem interest on \$418,900 at 6.875%. Then compute the prepaid interest for a closing on the 12th of a 30-day month.

4.37 † The Linden Street borrowers are \$1,400 short of their cash to close. Using §4.9, name two levers available and compute the effect of each.

H. The Loan File

4.38 † In your Appendix C workbook, build the first twelve rows of the Linden Street amortization schedule by hand, using only the one-line rule and rounding interest to the cent. Confirm the month-12 balance is \$361,757.88. Then rebuild the entire file at 10% down: compute the new loan amount, LTV, P&I, MI (assume the factor falls to 0.32% at 90% LTV), PITI, both ratios, and the change in cash to close. State which single line surprises you most.