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Each year a certain amount of money is deposited in an account which pays an annual interest rate of r so that at the end of each
year the balance in the account is multiplied by a growth factor of x = 1 + r. $1,000 is deposited at the start of the first year, an
additional $300 is deposited at the start of the next year, and $500 at the start of the following year.
Write an expression for the value of the account at the end of three years in terms of the growth factor x.

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The polynomial expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500x

Interest earned per year, x = 1 + r

First year :

  • deposit = $1000

Year end balance = 1000 × x = 1000x

Second year :

  • Initial balance = 1000x + 300

Year end balance = (1000x + 300)x = 1000x² + 300x

Third year :

  • Initial balance = 1000x² + 300x + 500

Year end balance = (1000x² + 300x + 500)x = 1000x³ + 300x² + 500x

Therefore, the expression which represents the value of the account at the end of three years is 1000x³ + 300x² + 500

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