Question

a new car is purchased for 25000 dollars. the value of the car depreciates at 8.25% per year. what will the value of the car be, to the nearest cent, after 15 years?

Explanation:

Step1: Define depreciation formula

La fórmula de depreciación exponencial es $A = P(1 - r)^t$, donde:

• $P = 25000$ (valor inicial),
• $r = 0.0825$ (tasa de depreciación),
• $t = 15$ (años).

Step2: Sustituir valores en la fórmula

$A = 25000(1 - 0.0825)^{15}$

Step3: Calcular factor de depreciación

Primero calculamos $1 - 0.0825 = 0.9175$, luego elevamos a la 15ª potencia: $0.9175^{15} \approx 0.2846$

Step4: Calcular valor final

$A = 25000 \times 0.2846 \approx 7115.00$

Answer:

7115.00 dólares