Which payment frequency results in the highest total annual cost for premiums according to the provided calculations?

When assessing the total annual cost of premiums based on the payment frequency, the semi-monthly option is typically the highest due to its more frequent payment schedule. This frequency requires policyholders to make payments 24 times a year, which often results in higher total premiums because the insurer may charge additional fees for the increased administrative costs associated with processing more payments.

In contrast, annual payments, while still accumulating a total premium, are usually offered at a lower rate because the insurer receives the full premium upfront, reducing their risk and administrative burden. Similarly, semi-annual and quarterly payments often have lower total annual costs compared to the semi-monthly frequency, as they involve fewer transactions and therefore less associated cost for the insurance provider.

Thus, with the semi-monthly option requiring more frequent payments, it combines both more payments and a greater potential for associated fees, leading to the highest total annual cost for premiums.