You are a new loan officer with Alpha Mortgage, and the manager of the loan depa
ID: 2787221 • Letter: Y
Question
You are a new loan officer with Alpha Mortgage, and the manager of the loan department has just presented a problem to you. He is unable to complete the APR calculation on an adjustable rate mortgage which a borrower applied for yesterday. The loan features initial payments based on a 10 percent rate of interest, while the current composite rate on the loan is 13 percent. No discount points have been paid by any party to the transaction, and any difference between borrower payments and the interest payment required at the composite rate will be accrued in the mortgage balance in the form of negative amortization. The mortgage amount desired by the borrower is $65,000 for a 30-year term, but a one-time mortgage insurance premium of $2,400 is being funded as a part of the loan amount, making the total loan balance $67,400. The borrower is paying $1,600 in prepaid finance charges at closing a. Determine the APR, assuming that the ARM is made with a 2 percent annual and 5 percent over-the-life interest rate cap b. In what way does the APR disclosure aid the borrower in understanding the terms of this specific loan agreement? What are some of the problems with the APR calculations on ARMs?Explanation / Answer
Answer (a) Now we have an ARM with the following characteristics:
Year
Composite Rate(Uncapped)
Composite (Capped)
Monthly Payments$
Monthly Interest(13%/12) $
Montly Amort $
Annual Amort $
* Assumes market interest rate equals 13% at beginning of year 2.
**Actual payment > monthly interest at this point. Hence payments have reached the maximum knowable (worst case scenario) amount as of the date of origination.
To solve for the APR:
1. Find the net outflow at close: $67,400 - $1,600 = $65,800
2. Set up the cash flow equation: $65,800 = PV of actual borrower payments (years 1-30).
3. Find the IRR which equates the PV of payments to $65,800.
4. The IRR solution (13.33%) is then rounded to 13.375%.
Answer (b) The disclosures must be completed three days after application is made by the borrower. The APR disclosure aids the borrower in understanding the effective cost of credit with all fees and charges added to the loan. It makes comparison between loans easier. However, the APR on an ARM will almost certainly not reflect the true cost of funds to the borrower, indeed, the APR on an ARM assumes that the composite rate on the ARM will remain constant over the life of the loan and generally, this is not the case.
Year
Composite Rate(Uncapped)
Composite (Capped)
Monthly Payments$
Monthly Interest(13%/12) $
Montly Amort $
Annual Amort $
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