Multiplication of Polynomials Application Help Needed

Hello,

I am hoping someone can help me to see what I'm doing wrong. I am an adult trying to learn algebra on my own after having been out of school for a long time. There is a textbook applied algebra problem in the Polynomials and Exponents chapter. The answer is given, but I can't see what I'm doing wrong in getting a different answer. Here is the problem:

Periodic Deposits.
At the beginning of each year for five years, an investor invests $10 in a mutual fund with an average annual return of r.
If we let x = 1 + r, then at the end of the first year (just before the next investment), the value is 10x dollars.
Because $10 is then added to the 10x dollars, the amount at the end of the second year is (10x + 10)x dollars.
Find a polynomial that represents the value of the investment at the end of the fifth year.
Evaluate this polynomial if r = 10%.

The given answer is 10x^5 + 10x^4 + 10x^3 + 10x^2 + 10x, $67.16.

The answer I got was 10x^5 + 10x^4.

A chart of my thinking (x = 1 + r):

Beginning of Year -I- Avg Return -I- End of Year Value
1 r 10x
2 r (10x + 10)x
3 r (10x^2 + 10x)x
4 r (10x^3 + 10x^2)x
5 r (10x^4 + 10x^3)x

And that final Value = 10x^5 + 10x^4.

Please, what am I doing wrong? Thank you so much to anyone who spends the time to help me.

Have a great day.

Jim

 

You are correct: at end of year 1, value = 10x.
You are correct: at end of year 2, value = (10x + 10)x [note: first term is prior year end value]
So - end of year 3, first term is its prior year end value, which = (10x + 10)x
giving [(10x + 10)x + 10]x = 10x^3 + 10x^2 + 10x
Rinse and repeat.