An insurance company offers a health policy with a base premium equal to $18\%$ of the sum insured. A loading of $12\%$ of the base premium is added for administrative expenses, and a tax of $5\%$ is applied on the sum of the base premium and the loading. An early‑payment discount of $3\%$ is given on the total after tax. A group of 25 employees each purchase a policy with a sum insured of ₦2,000,000.

(a) Calculate the total amount the group pays annually.

(b) If the insurer's cost per policy is $20\%$ of the sum insured and it wishes to earn a profit margin of $20\%$ on this cost, what discount (or surcharge) percentage should be applied, keeping all other rates unchanged, to achieve the target profit? Express the required adjustment as a percentage (a negative value indicates a surcharge).

Question

An insurance company offers a health policy with a base premium equal to $18\%$ of the sum insured. A loading of $12\%$ of the base premium is added for administrative expenses, and a tax of $5\%$ is applied on the sum of the base premium and the loading. An early‑payment discount of $3\%$ is given on the total after tax. A group of 25 employees each purchase a policy with a sum insured of ₦2,000,000.

(a) Calculate the total amount the group pays annually.

(b) If the insurer's cost per policy is $20\%$ of the sum insured and it wishes to earn a profit margin of $20\%$ on this cost, what discount (or surcharge) percentage should be applied, keeping all other rates unchanged, to achieve the target profit? Express the required adjustment as a percentage (a negative value indicates a surcharge).

Accepted Answer

Total paid: ₦10,266,480; required discount: -13.4\% (a 13.4\% surcharge)

Neco 2017 Commerce Question 25

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