4. A mortgage company offers borrowers a 4% annual interest rate on the one-year ARM that is amortized for 30 years. The index rate is forecast to be 5% for next year and the margin on this loan is 2%. The annual interest rate adjustment cap is 2%. What is the adjusted interest rate for the second year? What are the monthly payments for year 1 and 2 if $200,000 is borrowed? (Remember to use the balance as the new PV for 2nd year.)

For year 1,

PV = $200,000

r = 4% / 12 = 0.3333%

n = 30 x 12 = 360

Monthly payment = 200,000 x 0.003333 / [1 - (1 + 0.003333)-360]

= $954.83

For year 2,

n = 360 - 12 = 348

Balance = P x [1 - (1 + r)-n] / r

= 954.83 x [1 - (1 + 0.003333)-348] / 0.003333

= $196,477.93

The interest rate will be the lower of the previous year rate plust he annual rate cap or the index rate plus the margin.

The index rate plus the margin is 5% + 2% = 7%, while the previous rate plus the cap is 4% + 2% = 6%. The adjusted rate for the second year will be 6%

Monthly rate = 6% / 12 = 0.5%

PV = $196,477.93

r = 0.5%

n = 348

Monthly payment for year 2 = 196,477.93 x 0.005 / [1 - (1 + 0.005)-348]

= $1,192.63

Q5: What is the expected yield if you hold the ARM in Q4 for only two years?