Using Table 19-1 and Table 19-2, calculate the annual, semiannual, quarterly, and monthly premiums (in $) for the life insurance policy. Round your answers to the nearest cent.
| Face Value of Policy | Sex and Age of Insured | Type of Policy | Annual Premium | Semiannual Premium | Quarterly Premium | Monthly Premium |
|---|---|---|---|---|---|---|
| $70,000 | male-40 | whole life | $\square$ |$\square$ | $\square$ | $\square$ |
Answer (2)
Calculate the annual premium from the semiannual premium: 2 × $990.44 = $1980.88 .
Calculate the annual premium from the quarterly premium: 4 × $495.22 = $1980.88 .
Calculate the annual premium from the monthly premium: 12 × $171.42 = $2057.04 .
Average the three annual premiums to account for rounding differences: ( $1980.88 + $1980.88 + $2057.04 ) /3 = $2006.27 . The annual premium is $2006.27 .
Explanation
Problem Analysis We are given the semiannual, quarterly, and monthly premiums for a life insurance policy and need to calculate the annual premium. We will calculate the annual premium based on each of these values and then compare the results.
Annual Premium from Semiannual Premium First, let's calculate the annual premium based on the semiannual premium. Since there are two semiannual periods in a year, we multiply the semiannual premium by 2: 2 × $990.44 = $1980.88 So, based on the semiannual premium, the annual premium is $1980.88.
Annual Premium from Quarterly Premium Next, let's calculate the annual premium based on the quarterly premium. Since there are four quarters in a year, we multiply the quarterly premium by 4: 4 × $495.22 = $1980.88 So, based on the quarterly premium, the annual premium is $1980.88.
Annual Premium from Monthly Premium Now, let's calculate the annual premium based on the monthly premium. Since there are twelve months in a year, we multiply the monthly premium by 12: 12 × $171.42 = $2057.04 So, based on the monthly premium, the annual premium is $2057.04.
Calculating the Average Annual Premium We have three different values for the annual premium: $1980.88 (from semiannual), $1980.88 (from quarterly), and $2057.04 (from monthly). The values differ due to rounding. To find the most accurate annual premium, we will calculate the average of these three values: ( $1980.88 + $1980.88 + $2057.04 ) /3 = $6018.80/3 = $2006.266666... Rounding to the nearest cent, we get $2006.27.
Final Answer Therefore, the annual premium for the life insurance policy is approximately $2006.27.
Examples
Understanding insurance premiums can help you budget for your financial future. For example, if you're planning to purchase a home, knowing how to calculate annual insurance costs from monthly payments allows you to accurately estimate your yearly expenses. This skill is also useful when comparing different insurance policies to find the most cost-effective option. By understanding these calculations, you can make informed decisions about your financial planning and ensure you're adequately covered without overspending.
The annual premium for the life insurance policy is approximately $2006.27, calculated from the semiannual, quarterly, and monthly premiums by averaging the derived values. Each premium type provides a different annual estimate, and averaging helps account for rounding differences.
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