NMLS Mortgage Finance and Calculations Questions and Answers 1 — Questions and Answers
Question 1: A borrower obtains a $320,000 loan with a fixed interest rate of 6.75%. If their closing is on May 22nd, and their first mortgage payment is due on July 1st, how much per diem interest will they need to pay at closing for the month of May? (Assume a 365-day year and that May has 31 days).
- $591.78 (Correct answer)
- $650.96
- $532.61
- $1,832.88
Correct answer: $591.78
To calculate per diem (daily) interest, first find the annual interest: $320,000 * 6.75% = $21,600. Then, find the daily interest: $21,600 / 365 days = $59.178. The borrower pays interest for the day of closing through the last day of the month. In May (31 days), this period is 10 days (May 22, 23, 24, 25, 26, 27, 28, 29, 30, 31). The total per diem interest is $59.178 * 10 days = $591.78.
Question 2: A home is purchased for $450,000. The borrower makes a down payment of $67,500. What is the Loan-to-Value (LTV) ratio?
- 90%
- 15%
- 85% (Correct answer)
- 80%
Correct answer: 85%
The Loan-to-Value (LTV) ratio is calculated by dividing the loan amount by the lesser of the property's appraised value or sales price. First, determine the loan amount: $450,000 (Sales Price) - $67,500 (Down Payment) = $382,500 (Loan Amount). Then, calculate the LTV: $382,500 / $450,000 = 0.85, or 85%.
Question 3: A prospective borrower has a gross monthly income of $7,500. Their proposed monthly housing payment (PITI) is $2,025. What is the borrower's housing expense ratio (front-end DTI)?
- 32%
- 27% (Correct answer)
- 28%
- 36%
Correct answer: 27%
The housing expense ratio, also known as the front-end debt-to-income (DTI) ratio, is calculated by dividing the total monthly housing payment (PITI) by the gross monthly income. The calculation is: $2,025 / $7,500 = 0.27, which is 27%.
Question 4: A borrower is obtaining a loan for $280,000. To lower their interest rate, they are paying 2 discount points at closing. What is the total cost of the discount points?
- $2,800
- $7,000
- $4,200
- $5,600 (Correct answer)
Correct answer: $5,600
One discount point is equal to 1% of the loan amount. In this scenario, the borrower is paying 2 points, which is 2% of the loan amount. The calculation is: $280,000 * 0.02 = $5,600.
Question 5: Which of the following is true regarding the principal and interest portions of a monthly payment on a 30-year, fully amortizing, fixed-rate loan?
- The principal and interest portions remain equal throughout the loan term.
- The principal portion is highest in the early years and decreases over time.
- The interest portion is highest in the early years and decreases over time. (Correct answer)
- Both the principal and interest portions increase over the life of the loan.
Correct answer: The interest portion is highest in the early years and decreases over time.
In a fully amortizing loan, the payment is structured so that in the beginning of the loan term, a larger portion of the payment goes toward interest because the outstanding principal balance is at its highest. As the principal is paid down over time, the interest portion of each subsequent payment decreases, and the principal portion increases.
Question 6: A borrower has a 5/1 ARM with an initial interest rate of 4.5% and a 2/2/5 cap structure. The margin is 2.75%. At the first adjustment, the index is 3.0%. What will the borrower's new interest rate be?
- 6.5%
- 4.5%
- 5.75% (Correct answer)
- 7.25%
Correct answer: 5.75%
First, calculate the fully indexed rate by adding the margin and the index: 2.75% (Margin) + 3.0% (Index) = 5.75%. Next, apply the periodic adjustment cap. The initial cap is 2%, meaning the rate cannot increase by more than 2% at the first adjustment: 4.5% (Start Rate) + 2.0% (Cap) = 6.5%. The new rate will be the lesser of the fully indexed rate (5.75%) and the maximum allowed by the cap (6.5%). Therefore, the new interest rate is 5.75%.
