Question

A college student has been looking for 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).
a) 12 | 31
b) 24 | 51
c) 36 | 69
d) 48 | 94

Answer 1

The third tire, n=36, p=94, has the minimum equivalent uniform monthly cost = 2.2218

Explanation:

The interest rate is 10%

Monthly interest rate, i = 10/12 = 0.833%

The equivalent monthly cost for each tire= Tire Price*(A/P, i, n)

equivalent monthly cost=price*(i*(1+i)^n)/((1+i)^n -1)

Equivalent monthly cost of first tire = 31(A/P, i, n)

For the first alternative, n=12, price =31

Equivalent monthly cost of the first tire= 31(A/P,0.8333%, 12)

= 31*[{0.008333(1.008333)^12}/{(1.008333)^12 - 1}]

=31* 0.0879

Equivalent monthly cost of the first tire = 2.7249

Equivalent monthly cost of second tire = 51(A/P, i, n)

For the second alternative, n=24, price = 51

Equivalent monthly cost of the second tire = 51(A/P,0.8333%, 24)

= 51*[{0.008333(1.008333)^24}/{(1.008333)^24 -1}]

=51* 0.0461

Equivalent monthly cost of the second tire= 2.3511

Equivalent monthly cost of third tire = 69(A/P, i, n)

For the third alternative, n=36, price=69

Equivalent monthly cost of the third tire = 69(A/P,0.8333%, 36)

= 69*[{0.008333(1.008333)^36}/{(1.008333)^36-1}]

=69* 0.0322

Equivalent monthly cost of the third tire = 2.2218

Equivalent monthly cost of the fourth tire = 94(A/P, i, n)

For the fourth tire, n= 48, price = 98

Equivalent monthly cost of the fourth= 94(A/P,0.8333%, 48)

= 94*[{0.008333(1.008333)^48}/{(1.008333)^48-1}]

=94* 0.0253

Equivalent monthly cost of the fourth tire = 2.3782

The third tire, n=36, p=94, has the minimum equivalent uniform monthly cost = 2.2218