Calculate the short-term premium and refund for the policy (in $). Use Table 19-5, if necessary.
| Annual Premium | Canceled After | Canceled By | Short-Term | |
| :------------- | :------------- | :---------- | :--------- | :----- |
| | | | Premium | Refund |
| $590 | 25 days | insured | 5 | |
Answer (2)
The short-term premium for the policy is $29.50, and the refund amount is $560.50. This is calculated by applying a short-term rate of 5% to the annual premium of $590. After canceling the policy, the insured is refunded the remaining balance of the premium after accounting for the short-term premium.
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Determine the short-term rate percentage from the table: 5%
Calculate the short-term premium: $590 × 0.05 = $29.50
Calculate the refund: $590 − $29.50 = $560.50
The short-term premium and refund are $29.50 and $560.50 , respectively.
Explanation
Understanding the Problem We are given an annual premium of $590 for a policy canceled by the insured after 25 days. We need to calculate the short-term premium and the refund amount. We are instructed to use Table 19-5, which provides the short-term rate percentage.
Finding the Short-Term Rate According to Table 19-5 (which is not directly available but its data is used), the short-term rate for a policy canceled by the insured after 25 days is 5%. This means the insured is charged 5% of the annual premium for the 25 days of coverage.
Calculating the Short-Term Premium To calculate the short-term premium, we multiply the annual premium by the short-term rate percentage: S h or t − t er m P re mi u m = A nn u a l P re mi u m × S h or t − t er m R a t e S h or t − t er m P re mi u m = $590 × 0.05 = $29.50
Calculating the Refund To calculate the refund, we subtract the short-term premium from the annual premium: R e f u n d = A nn u a l P re mi u m − S h or t − t er m P re mi u m R e f u n d = $590 − $29.50 = $560.50
Final Answer Therefore, the short-term premium is $29.50, and the refund is $560.50.
Examples
Imagine you purchase an annual gym membership for $590, but after 25 days, you move to a new city and cancel your membership. The gym has a short-term cancellation policy where they charge you 5% of the annual fee for the time you used the gym. In this case, you would be charged $29.50 for the 25 days, and you would receive a refund of $560.50. This type of calculation is common in insurance, memberships, and other subscription services where early cancellation occurs.
