The correct answer is 9.57%. but I want to know how to solve it 5.6 A certain el

Question

The correct answer is 9.57%. but I want to know how to solve it

5.6 A certain electrical appliance is sold with a 5-year guarantee. This provides that the full purchase price is refunded if the product fails within 2 years, and half of the purchase price is refunded if the product fails in the following 3 years. A study shows that out of a typical batch of 100 items, there will be 2 failures in the first year, 3 failures in the second year and 4 failures per year after that. Assuming that interest is a constant 5% and that reimbursement is made at the end of the year of failure, what is the cost of this guarantee to the manufacturer, as a percentage of the purchase price?

Explanation / Answer

The correct answer would be as follows:-

Years Failures PV Factor PV            1            2.00            0.95           1.90            2            3.00            0.91           2.72            3            4.00            0.86           3.46            4            4.00            0.82           3.29            5            4.00            0.78           3.13 Total         14.51 Less: Rate of Interest           5.00 Cost of Gurantee           9.51

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