Polynomial Homework Help!!

Question

I have another question now... I've tried doing it different ways, but I'm just not sure. I'm looking for an explanation, not just an answer, please :) It's like this:

 

Suppose two brothers each make three deposits in accounts earning the same annual interest rate r (expressed as a decimal).

Porter, Mark J.                                            Porter, Tom R.                                

Date             Transaction        Amount  |  Date        Transaction     Amount

1/1/97          Deposit                 $6000     | 1/1/97      Deposit            $4000

1/1/98          Deposit                 $8000     | 1/1/98      Deposit            $5000

1/1/99          Deposit                 $9000     | 1/1/99      Deposit            $7000

Mark's account is worth 6000(1+r)³+8000(1+r)²+9000(1+r) on January 1, 2000. Find the value of Tom's account on January 1, 2000. Then find the total value of the two accounts on January 1, 2000. Write the total value as a polynomial in standard form.

 

Ok, so here's what I'm thinking: since Mark's account is worth 6000(1+r)³+8000(1+r)²+9000(1+r) on January 1, 2000, then Tom's would be worth 4000(1+r)³+5000(1+r)²+7000(1+r) on January 1, 2000... right? Because they have the same interest rate? So that's already simplified enough, or would I change it to:

(4000+4000r)³+(5000+5000r)²+(7000+7000r)                <--- I'm distributing

Umm... then I don't know where to go from there, if I'm even on the right track. I know that in the end, when I got Tom's account's value, I would end up adding Tom's and Mark's values together.

I'm just really confused. Please explain? 

Answer 1

First, THX for asking for an explanation, not just an answer!

Yes, the interest rate is the same.  So, you answered the question, “Find the value of Tom's account on January 1, 2000.”

Now, to add the two values (and since r is not given), factor only the yearly deposits of each and keep the (1+r)^n values for each year:

      [6000+4000](1+r)^3 + [8000+5000](1+r)^2  =  [9000+7000][1+r)

        10000(1+r)^3 + 13000(1+r)^2 + 16000(1+r)
 
note:  (1+r)^3  is  (1+r)(1+r)(1+r) so you didn't distribute correctly (do not put 4000 inside parenthesis)