What type of premium is charged for closed-end transactions where the premium is added to the principal of the loan?

The correct choice in this scenario is single premium. This type of premium is charged for closed-end transactions where the premium amount is added directly to the principal of the loan. A single premium serves to streamline the payment process by consolidating the cost into one lump sum, which is then financed along with the loan amount. This means that the borrower pays the premium as part of the total loan rather than making separate payments.

In contrast, the other types of premiums mentioned would not be applicable for a closed-end transaction where the premium is added to the principal. For example, an annual premium is typically paid on a yearly basis rather than being added to the loan amount upfront, while a monthly outstanding balance premium reflects a variable cost that changes with the loan balance and does not involve a one-time addition to the principal. Installment premiums imply payment of the premium through a series of payments rather than incorporating it into the loan's principal. Thus, in the context of this question, single premium is the most accurate description of the premium structure outlined.