A borrower received a 30-year ARM mortgage loan for $120,000. Rate caps are 3/2/6 (first adjustment/subsequent adjustments/total over the life of the loan). The start rate was 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is the LIBOR, which, for this exercise, let’s say was 3.00% at the start of the loan, 5.00% at the end of the first year, and 4.50% at the end of the second year. The margin on the loan is 3.00%, which remains the same for the duration of the loan.

Question

A borrower received a 30-year ARM mortgage loan for $120,000. Rate caps are 3/2/6 (first adjustment/subsequent adjustments/total over the life of the loan). The start rate was 3.50% and the loan adjusts every 12 months for the life of the mortgage. The index used for this mortgage is the LIBOR, which, for this exercise, let’s say was 3.00% at the start of the loan, 5.00% at the end of the first year, and 4.50% at the end of the second year. The margin on the loan is 3.00%, which remains the same for the duration of the loan. 
1.What’s the initial rate (start rate) and what is the interest rate after the first year?
What is the fully indexed rate after the second year?
What is the borrower’s interest rate after the second adjustment?
What is the maximum interest rate this loan could have?
What would the LIBOR have to be to obtain that interest rate?