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

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

Step-by-step 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