Question

An insurance agent gets commission of 20% on first year premium, 6% on second and third year’s premium and 4% on subsequent year premium on an insurance policy of Rs.40,000. Annual rate of premium being is Rs.30 per thousand. Find the total earning of the agent for which 5 annual premiums have been paid.
(a) Rs.680
(b) Rs.580
(c) Rs.480
(d) Rs.380

Answer 1

Hint: Find the annual premium which is the product of annual rate of premium and the rate of insurance policy. Find the commission for each year which is the percentage given on annual premium. The total earning is the sum of the commission up till 5 years.

Complete step-by-step answer:
Commission of \[{{1}^{st}}\] year premium = 20%
Commission of \[{{2}^{nd}}\] year premium = 6%
Commission of \[{{3}^{rd}}\] year premium = 6%
Commission on subsequent years = 4%
Rate of the insurance policy = Rs.40,000
Annual rate of premium = Rs.30 per thousand.
Annual premium = Annual rate of premium \[\times \] rate of insurance policy.
\[\therefore \] Annual premium = \[\dfrac{30}{1000}\times 40,000\]= Rs.1200.
\[\therefore \] Commission for \[{{2}^{nd}}\] year and \[{{3}^{rd}}\] year = 2 \[\times \] 6% \[\times \] annual premium
\[\therefore \] Commission for \[{{2}^{nd}}\] year and \[{{3}^{rd}}\] year = \[2\times \dfrac{6}{100}\times 1200\] = Rs.144
\[\therefore \] Commission for \[{{4}^{th}}\] year and \[{{5}^{th}}\] year = 2 \[\times \] 4% \[\times \] annual premium
\[\therefore \] Commission for \[{{4}^{th}}\] year and \[{{5}^{th}}\] year = \[2\times \dfrac{4}{100}\times 1200\] = Rs.96
\[\therefore \] Total earning is the commission for all these 5 years.
\[\therefore \] Total earning = 240 + 144 + 96 = Rs.480.
Thus the total earning of the agent for which 5 annual premiums have been paid is Rs.480.
\[\therefore \] Option (c) is the correct answer.

Note: Insurance premium is a monthly or annual payment made to an insurance company to keep the policy active. It can be any insurance like health insurance, life insurance, auto insurance etc. Any insurance policy comes up with many premium payment options. We must read the question carefully, it is given that commission is 6% for second and third year’s premium. Most often in a hurry, students miss the third year and consider only the second year. Then, as it is given for subsequent years, they might take 4% for third year. This mistake will make the whole solution wrong.