The original value of Bob's 2020 Toyota Camry was $27,750. It depreciated in price at a rate of 7.2% per year.

How much is it worth after a decade?

1 answer

To calculate the depreciation of Bob's 2020 Toyota Camry over a decade (10 years) at a rate of 7.2% per year, we can use the formula for exponential depreciation:

\[ V = P(1 - r)^t \]

where:

  • \( V \) is the value after time \( t \),
  • \( P \) is the original value,
  • \( r \) is the depreciation rate (as a decimal),
  • \( t \) is the time in years.

In this case:

  • \( P = 27750 \)
  • \( r = 0.072 \)
  • \( t = 10 \)

Substituting the values into the formula:

\[ V = 27750(1 - 0.072)^{10} \] \[ V = 27750(0.928)^{10} \]

Now, calculating \( (0.928)^{10} \):

\[ (0.928)^{10} \approx 0.5132 \quad (\text{using a calculator}) \]

Now, substituting back into the equation:

\[ V \approx 27750 \times 0.5132 \approx 14249.58 \]

Therefore, the approximate value of Bob's 2020 Toyota Camry after a decade is $14,249.58.