Question

Christmas tree shearing costs average $60 per acre per year for the third through the eighth years of an eight year rotation. At 9.5% interest these costs accumulate to how much by the time the trees are harvested? Assume that the costs occur at the end of the year.

Answer 1

Answer:

$457

Explanation:

The question is to determine the future cost accumulated by the time they are harvested. The Formula therefore is the Future Value formula

FV= P x (1+r)∧n

Where FV= Future Value

P= Cost Average in the 3rd year

r= rate of 9.5%

n= period or year

To get FV, we start the calculation from year 3 where there are only 5 years left until the harvest.

FV= Year 3 Cost (1+r)∧5+ Year 3 Cost (1+r)∧4+Year 3 Cost (1+r)∧3+Year 3 Cost (1+r)∧2+Year 3 Cost (1+r)∧1 + Year 3 Cost (1+r)∧0

FV= 60 (1+0.095)∧5+ 60 (1+0.095)∧4+60 (1+0.095)∧3+60 (1+0.095)∧2+60 (1+0.095)∧1+60 (1+0.095)∧0

FV= 94.45+86.26+78.78+71.94+60

FV=$457

The value of the trees by the eighth year when they are harvested will be $457