Response to the following problem:
An FI is planning the purchase of a $5 million loan to raise the existing average duration of its assets from 3.5 years to 5 years. It currently has total assets worth $20 million, $5 million in cash (0 duration), and $15 million in loans. All the loans are fairly priced.
a. Assuming it uses the cash to purchase the loan, should it purchase the loan if its duration is seven years?
b. What asset duration loans should it purchase in order to raise its average duration to five years?