Alex wants to borrow a sum of $1,000,000 to finance the expansion of her business. She had spoken to two banks, Banks A and B about it.

Bank A is offering a variable rate loan package with a teaser rate for the first two years of the loan. The loan is expected to be fully repaid in five years. details below shows the annual loan rates applicable at each year of the loan.

year 1 : 0.5%

year 2: 1%

year 3: 5%

year 4: 7.5%

year 5: 10%

The yearly payment of a variable rate loan is calculated as if it is a fixed rate loan on the outstanding loan balance and time remaining on the loan, whenever the variable rate is changed. The variable rate is reset at the beginning of each year.

To sweeten the deal, Bank A is offering Alex a special deal, where the first payment of the loan will happen at the end of the second year (but interest on the loan is still accruing).

For Bank B, they are offering a fixed rate of 3.5% for a five-years loan.

Assume all loan repayments are made at the end of each year for both Banks A and B.

Build a model for both Bank A and B to evaluate the cash flows regarding the loan.

If the prevailing interest rate is 1.2% (for all maturities), use the model to evaluate the maximum fixed rate that can be charged by Bank B before both loans become comparable.