Question

A basic ARM is made for $500, 000 at an initial interest rate of 3% with 2 discount points for 10 years. Payments are to be reset each year. The borrower believes that the interest rate at the beginning of year 2 will increase to 9 percent. Assuming that fulling amortizing is made and negative amortization is allowed if payment cap reached. If the ARM loan has a maximum 5% annual increase payment cap, what is the expected yield to the lender if the ARM loan is repaid after two years?

Answer 1

Solution. :-

ARM is adjustable rate mortgage

Max. cap is also given. with 5% increase

Initial interest rate = 3% + 2 discount points = 5%

The rate at the start of 2nd year or end of 1st year is 9% (given)

Yearly payment in 1st year = PMT(5%, 10 , - 500000,0) in excel would give = $64752

Interest paid in 1 year = 5%*500000 = 25000.

Therefore Principal payment = 64752-25000 = $39752

Balance after 1st year = 500000-39752 = 460248

Now interest paid in 2nd year = 460248*9% = 41422

Total interest paid upto 2 years = 41422+25000 = 66422

Let r be the interest yield paid ,

so (66422÷500000) = 13.28% in 2 years

So, we can say that (1+r)² = 1.1328

= (1+r) = 1.0643

Therefore r = 1.0643 - 1 = 0.0643 = 6.433%

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