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? (Choose the nearest value)

	a.	8.32%
	b.	5.81%
	c.	6.95%
	d.	7.62%

Answer 1

Ans : ARM is adjustable rate mortgage, means the rate of the mortgage is changed/adjust every year as given also on the basis of inflation index. Max. cap is also given. with 5% increase

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

Now, at the beginning of the 2nd year or end of 1st year the rate is expected to be 9%

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

Interest paid in 1 year = 5%*500000 = 25000. Principal paid = 64752-25000 = $39752

Balance remian to pay after 1st year = 500000-39752 = 460248

Now, on this amount , total interest paid in 2nd year = 460248*9% = 41422

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

Let r be the interest yield paid , so , we can say 66422/500000 = 13.28% in 2 years

So, we can say that (1+r)² = 1.1328 , on solving we get r = 6.95%

Option c is the correct ans.