Final answer:
A 90% Loan-to-Value (LTV) conventional mortgage would most likely require private mortgage insurance.
Step-by-step explanation:
The loan that would most likely require private mortgage insurance is option 2) a 90% Loan-to-Value (LTV) conventional mortgage. Private mortgage insurance (PMI) is typically required when the down payment on a house is less than 20% of the purchase price. In this case, the loan-to-value ratio is 90%, indicating that the borrower is making a down payment of only 10%.