Question

1. Victor brought a brand new car for 750,000. IF the value of the car depreciates 20% per year, what will it be worth during the fourth year?

2. Given the terms a10 = 3/512 and a15 = 3/16384 of a geometric sequence, find the exact value of the first term of the sequence.

Answer 1

For 1, use the depreciation formula of p(1 - r)^t.

p = price of the brand new car ($750,000)
r = rate of 20% turned into 0.02
t = time of (4) years

Now, we substitute the values of the variables for the numbers involved.

750,000(1 - 0.02)^4 =

Next, you subtract 0.02 from 1, and then you raise that total to the fourth power.

1 - 0.02 = 0.98 = 0.98^4

0.98^4 raised to the fourth power equals 0.92236816.

Now, since you have 0.92236816 in the parenthesis, you multiply 750,000 by 0.92236816.

750,000(0.92236816) = ?

Also, don't forget that 750,000(0.92236816) is also the same as:

750,000 x 0.92236816 = ?

I hope this helps for 1! :)

P.S. Don't forget the formula that I used for depreciation.