Honors Algebra II Problem?

chrisbsterchrisbster
in Science & Mathematics

The polynomial 1600X^3 + 1200X^2 + 800X represents Devone's savings from a summer job after thress years. The annual interest rate equals X - 1. Find the interest rate needed so he will have 4000$ after three years.

If I set the polynomial equal to 4000, then I have left out interest rate. Also, if it is asking me to craft my own interest rate, why would it give me an equation???

Help needed...

Update:

Philo...thank YOU SO MUCH

I reworked the problem and you were totally right, 0.05%.

I just got hung up on the phrasing of the question for some reason

THANKS!!! :)

Comments

  • philophilo

    If the interest rate is 5%, you multiply by 1.05 to do the compounding (think about it). The 1 is all of the amount and the .05 is the interest on the amount, so when you add the interest to the original, you get (1 + interest rate) TIMES the original. So the X in your equation is this growth factor, and X - 1 is the annual interest rate.

    So just solve 1600x^3 + 1200x² + 800x = 4000 for x (the growth factor), and then subtract x-1 to get the annual rate.

    Dividing out the 400, you have

    4x^3 + 3x² + 2x - 10 = 0

    Solving with TI-83 gives x = 1.0482328, so the annual rate must be at least 4.82328%.

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