Question

Your friend is able to deduct the cost of their new $13,300 computer from their taxes, but must provide an estimate of how much it will depreciate over the next 11 years. your friend asks you for help and tells you that the computer should depreciate at a continuous rate of 5% per year. what will their computer be worth in 11 years, to the nearest dollar?

Answer 1

To find the value of a computer after 11 years with continuous depreciation at a rate of 5% per year, use the exponential decay formula. The computer's value will be approximately $7675, rounded to the nearest dollar.

Step-by-step explanation:

To calculate the value of a computer after 11 years with a continuous depreciation rate of 5% per year, we can use the formula for exponential decay, which is V = P * e^(-rt), where V is the future value of the computer, P is the present value, e is the base of the natural logarithm, r is the rate of depreciation, and t is the time in years.

The present value of the computer is $13,300, the rate of depreciation is 5% or 0.05, and the time is 11 years. Thus, the calculation would be as follows:

1. Convert the percentage to a decimal: 5% => 0.05.
2. Apply the exponential decay formula: V = 13300 * e^(-0.05 * 11).
3. Calculate the future value: V ≈ 13300 * e^(-0.55) ≈ 13300 * 0.57695 ≈ $7675.

The computer will be worth approximately $7675, to the nearest dollar, after 11 years.