[10] A 3/1 hybrid ARM for $424,000 is to be made for 15 years with an initial pe

Question

[10] A 3/1 hybrid ARM for $424,000 is to be made for 15 years with an initial period MEY of 4%. The index is the 1-year CMT and the margin is 200bps. Interest rate caps are 2/6/3 (last cap is for the fixed-to-floating reset), and the payment cap is 20% with a 120% negative amortization cap. All payments are monthly and the mortgage is fully amortizing. Assume that the borrower never curtails the loan. 1. Also assume that the index on each anniversary of closing will be (date, index): (0,4%), (1,65%. (2,65%), (3, 7%) (4,75%), (5-30, 6.5%) A. 12] What are the payments in year 1? B. (1] What is the OLB at the end of year 3? C. [1] What are the payments in year 4? D. [6] If upfront variable fees are 3% of loan amount, and fixed fees are S2,000, what is the APR that the lender must disclose to the borrower? 2. (10] A homeowner purchases a property for $900,000. He finances the purchase with an 809 LTV, 30-year fully amortizing GPM carrying a 7% interest rate. A 20% rate of graduation will applied to monthly payments beginning year 2 and the beginning of year 3, only (payments years 3 and 4 and on are the same). The homeowner will sell the property after 8 years and does not curtail the loan ever. Upfront fees amount to 4% of the loan amount, plus $4,000 which were financed. A prepayment penalty of 3% applies. What is the effective cost of the loan?

Explanation / Answer

2.) Purchase Price =$900,000

LTV =80% => Loan Amount =0.80x900,000 =$720,000

Interest Rate =7% or 0.5833%

Graduated Payment Mortgage Rate =20% (beginning of Year 2 and Year 3)

Property to be sold after 8 years or 96 months

First we will determine the normal first payment (PMT) at stated rate of interest i.e.

720,000 = PMTx{{(1-(1+0.00583)-12)/0.00583} + 1.20x{(1-(1+0.00583)-12)/0.00583}x(1+0.00583)-12 + 1.202x{(1-(1+0.00583)-336)/0.00583}x(1+0.00583)-24}

720,000 = PMT x {11.5571 + 12.9336 + 184.2804}

720,000 = PMT x 208.7710

PMT = $3,448.75

Amount to be paid monthly in first year =$3,448.75

Amount to be paid monthly in second year =$3,448.75x1.20 =$4,138.50

Amount to be paid monthly in thid year and =$4,966.21

After making these payments till Year-8, Loan Outstanding =$668,018

Let y be the effective loan cost

720,000 = 0.04x720,000 + 4,000 + 3,448.75x{(1-(1+y)-12)/y} + 4,138.50x{(1-(1+y)-12)/y}x(1+y)-12 + 4,966.21x{(1-(1+y)-72)/y}x(1+y)-24 + 668,018x(1+y)-96

720,000 = 28,800 + 4,000 + 3,448.75x{(1-(1+y)-12)/y} + 4,138.50x{(1-(1+y)-12)/y}x(1+y)-12 + 4,966.21x{(1-(1+y)-72)/y}x(1+y)-24+ 668,018x(1+y)-96

687,200 = 3,448.75x{(1-(1+y)-12)/y} + 4,138.50x{(1-(1+y)-12)/y}x(1+y)-12 + 4,966.21x{(1-(1+y)-72)/y}x(1+y)-24+ 668,018x(1+y)-96

Solving for y using Trial and Error method,

For y=0.006, RHS =711,369

For y=0.007, RHS =662,106

For y=0.0065, RHS =686,208

For y=0.006478, RHS =687,200

Hence, Annual Effective Rate =0.006478x12 =0.0777 or 7.77%

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