Question

A college student has been looking for a new tires. The student feels that the warranty period is a good estimate of the tire life and that 10% interest rate is appropriate. Given 4 options find the minimum Equivalent Uniform Monthly Cost. (Note: the student wants to buy 4 tires) Hint use i/12 for computing the annual costs. Warranty time (months) Tire price (all 4 tires)

Warranty time (months)	Tire price (all 4 tires)
12	36
24	54
36	68
48	93

Answer 1

The college student wants to calculate equivalent uniform monthly cost of different alternative tiers. The warranty period can be taken as life period of different alternatives. The interest rate is 10% and monthly interest will be 10/12 = 0.8333%.

Now in this context the equivalent monthly cost of first alternative will be 36( A/P, i, n) = 36(A/P, 0.8333%, 12) = 36*[{0.008333(1.008333)^12}/{(1.008333)^12 - 1}] = 36* 0.0879 = 3.1614.

Similarly equivalent uniform monthly cost of 2nd alternative with 24 moths life is 54(A/P, i, n) = 54(A/P, 0.8333%, 24) = 54*[{0.008333(1.008333)^24}/{(1.008333)^24 -1}] = 54*0.0461 = 2.4894

Equivalent uniform monthly cost of third alternative with 36 moths life is 68(A/P, i, n) = 68(A/P, 0.8333%, 36) = 68*[{0.008333(1.008333)^36}/{(1.008333)^36 -1}] = 68*0.0322 = 2.1896

Equivalent uniform monthly cost of fourth alternative with 48 months life is 93(A/P, i, n) = 93(A/P, 0.008333, 48) = 93*[{0.008333(1.008333)^48}/{(1.008333)^48 -1}] = 93*0.0253 = 2.3529.

Therefore we get from the above calculations that equivalent uniform monthly cost of third alternative i.e whose life 36 months is lowest i.e 2.1896. According to this equivalent uniform monthly cost the student should chose third alternative i.e tiers with 36 moths warranty. The price of all 4 tiers is 68. The answer is tier with 36 months warranty and price is 68.