An Analysis of Prepayment Discounts

In many lines of fire and casualty insurance it is customary to issue policies for periods longer than one year to be paid for by a single premium at the date of issue. The usual periods are 3 and 5 years with the single premium for the former being 2 1/2 times the annual premium and that for the 5-year period, 4 times the annual premium. Looking at it superficially, the policyholder will probably believe that the 5-year plan is more to his advantage since a discount of 20% is given as contrasted with only 16~% for the 3-year plan. However, as will be shown subsequently, this conclusion in most instances is not valid when interest is taken into consideration (as should probably be done in all private insurance matters).