Determine the difference in the present worth values of the following two commodity contracts at an interest rate of 8% per year. a. Contract 1 has a cost of $10,000 in year 1; costs will escalate at a rate of 4% per year for 10 years. b. Contract 2 has the same cost in year 1, but costs will escalate at 6% per years for 11 years

$14,336

Explanation:

Calculation to Determine the difference in the present worth values

First step is to calculate Contract 1 present worth values

Contract 1 present worth values = 10,000{1 – [(1 + 0.04)/(1 + 0.08)]^10}/(0.08 – 0.04)

Contract 1 present worth values = 10,000{1 – [(1.04)/(1 .08)]^10}/( 0.04)

Contract 1 present worth values = $78,590

Second step is to Contract 2 present worth values

Contract 2 present worth values

= 10,000{1 – [(1 +0.06)/(1 +0.08)]^11}/(0.08 – 0.06)=

Contract 2 present worth values

= 10,000{1 – [(1 .06)/(1 .08)]^11}/( 0.02)

Contract 2 present worth values = $92,926

Now let calculate the difference in the present worth values

Present worth values Difference =$92,926-$78,590

Present worth values Difference =$14,336

Therefore the difference in the present worth values will be $14,336

i'ts proportional. if the inflation rate is 12% for example, the cpi will be 12% less.

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