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4 ) An insurance company pays its agent a commission at 20 % on the first year 's premium amount . The rate of commission reduce , to 6 % for the subsequent years . A customer purchased a policy premium at 5 % of the policy amount. Find the agent's total earning for the premium for the period of seven years.?
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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.
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4 ) An insurance company pays its agent a commission at 20 % on the first year 's premium amount . The rate of commission reduce , to 6 % for the subsequent years . A customer purchased a policy premium at 5 % of the policy amount. Find the agent's total earning for the premium for the period of seven years.?
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