Math Is Fun Forum

sachik

Member

Registered: 2008-02-28

Posts: 9

Geometric Sequence PLEASE HELP!!!

Hi everybody,

I really need help figuring this out, any help or feedback would be highly appreciated

" You purchased a car for $25,000. Its value depreciates at an average rate of 10% per year."

find an equation for the value of the car after n years

would i have to use the explicit or recursive formula....I have tried pluging in the values but the answers it gave me made no sense at all....

I know its value for the first 10 years:

after the 1st year its worth: 22,500
2nd: 20,250
3rd:18,225
4th:16,403
5th: 14,762
6th: 13,286
7th: 11, 957
8th: 10, 762
9th: 9, 686
10th: 8, 717

finding a formula for this seems very easy and obvious....but i just can't figure it out....its driving me crazy....i'm sure that after i see it i will realize how obvious it was....

so if someone could please please please help me find a formula, and explain to me how it works....I would highly appreciate that....

Thanks in advance,

Dennis Sachik

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Geometric Sequence PLEASE HELP!!!

Hello sachik,

This is an example where you would use a compound interest formula.

After the first year, the value is

After the second year,

After the third year,

.
.
.
After the nth year,

And here is your formula

And in general, the simple formula for compound interest:

Where

is the total value of the investment after n years,

is the principle (or initial) investment,

is the percentage interest (can be negative, as is the case in this problem)

is the number of years.

Last edited by Identity (2008-02-28 22:21:01)

sachik

Member

Registered: 2008-02-28

Posts: 9

Re: Geometric Sequence PLEASE HELP!!!

Thanks A LOT Identity, your information was very very helpful, I dont have to tear my hair out anymore :-)