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. The FI’s liabilities have an average duration of five years. All the loans are fairly priced.

a. Assuming it uses the cash to purchase the loan, should the FI purchase the loan if its duration is seven years?

b. What asset duration loans should the FI purchase to raise its average duration to five years?