1. The ABC company needs to borrow $3,200,000 and they have narrowed their choices to two loans:
   1. • Loan A j₂ = 6%, locked in and amortized over 10-years with semi-annual payments
      • Loan B j₂ = 5%, semi-annual payments of interest only are made over 10-years, with the principal repaid in one lump sum at the end of 10-years

a) In order to even consider Loan B, what rate of interest, j₂, must ABC earn on a sinking fund? (you may end up needing linear interpolation)

b) Lets suppose ABC ended up choosing Loan A. After 5 years they wish to refinance the loan at j₂ = 4%. There is no penalty for doing this, but the lender uses the sum-of-digits method to determine the outstanding balance. What is the revised semi-annual payment? What would be the revised payment if the amortization method was used to determine the outstanding balance? The lender says there is no penalty for refinancing the loan early, but there actually is a hidden penalty. What is the size of this hidden penalty?