# Thread: finding value of car

1. ## finding value of car

hello,

the value of a certain type of car depreicates 20% the first year and 5% each year afterwards. how would i find the value of 5 year old car of this tyoe which originally sold for $4000 can someone please demontrate how a question of this form is solved? 2. Originally Posted by sigma1 hello, the value of a certain type of car depreicates 20% the first year and 5% each year afterwards. how would i find the value of 5 year old car of this tyoe which originally sold for$4000

can someone please demontrate how a question of this form is solved?
Let $P_0$ be the original price

After one year the car loses 20% of P: $P_1 = 0.8P_0 = (1-0.2)P_0$

Thereafter the car loses 5% each year (let t be the time in years): $P_t = P_1(1-0.05)^{t-1}$

If we combine these expressions together we get the form $P_t = P_0(1-0.2)(1-0.05)^{t-1} = 0.8P_0 \cdot 0.95^{t-1}$

Since you know $P_0$ and $t$ you can substitute in order to find $P_5$

3. thanks alot, i would have tried to solve that from first principles..