An FI is planning the purchase of a $4 million loan to raise the existing average duration of its assets from 4.9 years to 6.4 years. It currently has total assets worth $22 million, $4 million in cash (0 duration), and $18 million in loans. All the loans are fairly priced.

a-1. Assuming it uses the cash to purchase the loan, calculate the duration of the existing loan. (Round your answer to 3 decimal places. (e.g., 32.161))

a-2. Assuming the FI uses the cash to purchase the loan and that the loan has a 8.4 year duration, calculate the resulting duration of the asset portfolio. (Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161))

a-3. Should it purchase the loan if its duration is 8.4 years?

b. What asset duration loans should it purchase in order to raise its average duration to 6.4 years? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16))