Answer :
The final value of the first model is found to be $43,945.31 and the final value of the second model of truck that sells for $29,000 and undergoes depreciation at a rate of 12% per year for 7 years is $11,851.59.
Let's break this problem down into two parts.
The first part deals with modeling the growth of an initial value through an interest rate over a certain amount of years. We start with an initial value of $18,000 which is increasing at a quarter of its value per year for 4 years.
To get the final value we use a compounding formula: Principal * (1 + rate)^time. Here, the principal is $18,000, the rate is 0.25 (or 25%) and the time is 4 years.
So the formula becomes: $18,000 * (1+0.25)⁴
which equals to $43,945.31 approximately.
The second part of the question follows similar logic but instead of growth, we're talking about depreciation, or decrease in value. In this scenario, imagine a truck that sells for $29,000 and depreciates at a rate of 12% per year for 7 years.
Again we use a similar formula to the one above but subtract the depreciation rate from 1, representing the percentage of the truck's value it retains each year.
The formula becomes: $29,000 * (1-0.12)⁷
which tapers out to be approximately equal to $11,851.59.
So, the final value of the first model is $43,945.31 and the final value of the second model is $11,851.59.
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