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.