Two bride designs have been proposed for the new interstate highway to cross Rio de Lubbock. A bridge constructed from wood will cost $6,000 and will last for 8 years. A bridge constructed from steel will cost $11,000 and will last for 20 years. Either bridge will have a 0 salvage value. at the end of its life. Use an interest rate of 8% and determine which material will be more economical for the construction of the bridge.

Uniform annual cost of wood design:Uniform annual cost of steel design:

Uniform annual cost A = $1,044.088

Uniform annual cost B= $1,120.374

Option A is cheaper because it has a lower equivalent annual cost

Explanation:

To determine the better of the two options, we would compare the equivalent annual cost of each options using a discount rate of 8% per annum

Uniform annual cost = PV/Annuity factor

Annuity factor = (1- (1+r)^(-n))/r

r- rate , n- years

Option A-

r- 8% , n- 8, PV - 6000

(1- (1.08)^(-8))/0.08= 4.62287

Equivalent Annual cost

= 6000/5.74663

Uniform annual cost=$1,044.088

Option B

Annuity factor = 1 -1.08^(-20)/0.08 =9.8181

Equivalent annual cost

= 11,000/9.8181

Uniform annual cost=$1,120.374

Option A is cheaper because it has a lower equivalent annual cost

month 1 start amount =$3287.90 interest=(3287.90x0.0145/12)3.97 total to pay=$3291.81 paid =$1200 balance =$2,091.87

month 2 starting amount= $2,091.87 interest =$25.28 total to pay =$2117.15 paid =$1200 balance $917.15

month 3 starting amount =$917.15 interest =$11.08 total to pay =$928.23 paid =$928.23 balance =$0 total to pay 1200+1200+928.23 = $3328.23 it will take 3 months to pay a total of $3328.23

rational decision making is a multi-step process for making choices between alternatives. the process of rational decision making favors logic, objectivity, and analysis over subjectivity and insight. the word “rational” in this context does not mean sane or clear-headed as it does in the colloquial sense.

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