4 ) An insurance company pays its agent a commission at 20 % on the fi...
Problem Statement
An insurance agent is paid a commission of 20% on the first year's premium amount and 6% for the subsequent years. A customer purchased a policy premium at 5% of the policy amount. Find the agent's total earnings for the premium for the period of seven years.
Solution
Calculation of Premium Amount
Let's assume that the policy amount is $100. Therefore, the premium amount for the first year would be $5 (5% of $100).
Calculation of Commission for the First Year
The commission for the first year would be 20% of the premium amount, which is:
Commission for the first year = 20% of $5 = $1
Calculation of Commission for the Subsequent Years
The commission for the subsequent years would be 6% of the premium amount, which is:
Commission for the subsequent years = 6% of $5 = $0.30
Calculation of Agent's Total Earnings for 7 Years
The premium amount for the subsequent years would be the same as the premium amount for the first year, which is $5. Therefore, the total premium amount for 7 years would be:
Total premium amount = $5 (for the first year) + $5 x 6 (for the subsequent years) = $35
The commission for the first year would be $1, and the commission for the subsequent years would be $0.30 per year. Therefore, the total commission for 7 years would be:
Total commission = $1 (for the first year) + $0.30 x 6 (for the subsequent years) x 6 = $11.40
Therefore, the agent's total earnings for the premium for the period of seven years would be:
Total earnings = Total premium amount + Total commission = $35 + $11.40 = $46.40
Conclusion
In conclusion, the agent's total earnings for the premium for the period of seven years would be $46.40. The commission rate for the first year is higher than the subsequent years, which is a common practice in the insurance industry.