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
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
