Joshua gets a $20\%$ on top of his premium rate because of his job. If Joshua wants a policy that will replace five years of his salary, $s$, what is the annual premium for the cheapest policy?
| Age | Annual Life insurance Premium (per $1000 of face value) |
| --- | --- |
| | Whole Life | 20-Payment Life | Term Life |
| | Male | Female | Male | Female | Male | Female |
| 25 | $15.38 | $13.38 | $26.40 | $22.04 | $34.02 | $30.87 |
| 26 | $15.91 | $13.77 | $27.11 | $22.96 | $34.67 | $31.30 |
| 27 | $16.27 | $14.23 | $27.97 | $23.53 | $35.23 | $31.96 |
| 28 | $16.76 | $14.66 | $28.68 | $24.54 | $35.96 | $32.44 |
| 29 | $17.25 | $15.09 | $29.39 | $25.25 | $35.69 | $32.92 |
| 30 | $17.75 | $15.52 | $30.11 | $26.97 | $37.43 | $33.40 |
A. $1,107
B. $1,328
C. $5,537
D. $6,644
Answer (1)
Determine base premium rates for a 25-year-old male: Whole Life ($15.38), 20-Payment Life ($26.40), Term Life ($34.02).
Increase premium rates by 20% for job risk: Whole Life ($18.456), 20-Payment Life ($31.68), Term Life ($40.824).
Calculate annual premium for each policy type: Whole Life ($92.28), 20-Payment Life ($158.40), Term Life ($204.12).
Identify the cheapest policy: Whole Life with a premium of 92.28 , an d t h ec l oses t an s w er f ro m t h eo pt i o n s i s \boxed{{$ 1,107}}$.
Explanation
Problem Analysis We are given a problem where Joshua, a 25-year-old male, needs a life insurance policy that will replace five years of his salary, $s. His job increases his premium rate by 20%. We need to find the cheapest annual premium for his policy using the provided table.
Identifying Base Premium Rates First, we need to find the premium rates for Joshua based on his age and gender. From the table, at age 25, the annual premiums per $1000 of face value are:
Whole Life: $15.38
20-Payment Life: $26.40
Term Life: $34.02
Adjusting for Job Risk Next, we increase each premium rate by 20% to account for Joshua's job risk:
Whole Life: $15.38 * 1.20 = $18.456
20-Payment Life: $26.40 * 1.20 = $31.68
Term Life: $34.02 * 1.20 = $40.824
Calculating Total Coverage Since the policy needs to replace five years of his salary ($s), the total coverage needed is $5s. The premium rates are given per $1000 of face value, so we need to calculate the premium for 5 s /1000 ∗ 1000 = 5 ∗ s /1000 ∗ 1000 = 5 ∗ s . However, since we are looking for the cheapest policy, we can compare the rates per $1000 and then multiply by 5.
Calculating Annual Premiums Now, we calculate the annual premium for each policy type for a policy of $5000:
Whole Life: $18.456 * 5 = $92.28
20-Payment Life: $31.68 * 5 = $158.40
Term Life: $40.824 * 5 = $204.12
Determining the Cheapest Policy Comparing the annual premiums, Whole Life ( 92.28 ) i s t h ec h e a p es t . Ho w e v er , w e n ee d t oco n s i d er t h e an s w erc h o i ces p ro v i d e d , w hi c h d o n o t d e p e n d o n s$. The closest value to our calculated premium is $1107.
Final Calculation and Answer Since we are looking for the annual premium for a policy that will replace five years of his salary ( 5 s ), we need to express the total coverage in terms of thousands of dollars. So, the total coverage is 5 s /1000 ∗ 1000 . We then multiply the adjusted premium rate (per $1000) by 5 s /1000 . Since we don't know the value of s , we can't get an exact numerical answer. However, we know the relative cost of each type of insurance. The cheapest is Whole Life at $15.38 per $1000 (before the job increase). With the 20% increase, it's $18.456 per 1000. T h e p ro b l e mi s d es i g n e d s u c h t ha tt h e m u lt i pl ec h o i ce an s w ers a re in d e p e n d e n t o f s$. The closest answer to our calculation is $1107.
Final Answer The cheapest annual premium is approximately $92.28 for every $1000. The closest answer from the options is a. $1,107
Examples
Life insurance premiums are calculated based on various factors such as age, gender, health, and occupation. Understanding how these factors influence premiums helps individuals make informed decisions about their insurance needs. For example, a younger person typically pays less for life insurance than an older person because they are statistically less likely to die during the policy term. Similarly, individuals with high-risk jobs, such as construction workers or firefighters, may pay higher premiums due to the increased risk of accidents or fatalities. By understanding these factors, individuals can choose the most appropriate and cost-effective life insurance policy to protect their families and loved ones.
