You have taken out a $100,000, one-year ARM. The teaser rate in the first year is 4.5% (annual). The index interest rate after the first year is 3.25% and the margin is 2.75%. (Note: the term on this ARM is 30 years). There is also a periodic (annual) rate cap of 1.00%. Given this information, determine the monthly mortgage payment you would be scheduled to make in month 1 of the mortgage loan's term.

Question

Quizplus · Accepted Answer

To determine the monthly mortgage payment, we need to:

1. Calculate the effective interest rate for the first year:
Effective rate = teaser rate = 4.5%

2. Calculate the new interest rate after the first year:
New rate = index rate + margin = 3.25% + 2.75% = 6%

3. Determine the maximum interest rate for year 2:
Max rate = new rate + cap rate = 6% + 1% = 7%

4. Calculate the monthly payment using the maximum interest rate, a term of 30 years, and a principal of $100,000:
Payment = (P * r) / (1 - (1 + r)^(-n))
where P = principal = $100,000
      r = monthly interest rate = (max rate / 12) = (7% / 12) = 0.58333%
      n = number of payments = term in months = (30 years * 12) = 360

Payment = (100000 * 0.0058333) / (1 - (1 + 0.0058333)^(-360))
Payment = $506.69

Therefore, the monthly mortgage payment you would be scheduled to make in month 1 of the mortgage loan's term is $506.69. The correct answer is B.

You Have Taken Out a $100,000, One-Year ARM