Laurel’s grandparents put money in a savings account for her college education. When she was born, they put in $5000. On each of her first three birthdays, they deposited an additional $1000. On her fourth birthday, they deposited $2500. There were no additional deposits or withdrawals. The bank account earns an annual interest rate of r.
How much money is in the account on Laurel’s fourth birthday after the $2500 deposit? Write your answer as a polynomial in terms of x where x = (1 + r).

Question

Laurel’s grandparents put money in a savings account for her college education. When she was born, they put in $5000. On each of her first three birthdays, they deposited an additional $1000. On her fourth birthday, they deposited $2500. There were no additional deposits or withdrawals. The bank account earns an annual interest rate of r.
How much money is in the account on Laurel’s fourth birthday after the $2500 deposit? Write your answer as a polynomial in terms of x where x = (1 + r).

precal · Answer

Nice grandparents

anonymous · Answer

I can only assume it is compounded annually from the information given. 

To solve this problem, the most simple method would be to just calculate quickly what the balance is after each year.

To get you started, 
1st year: 5000
multiply by X to find the balance after interest. Continue year by year until you arrive on the 4th birthday.

anonymous · Answer

M = P( 1 + i )n

M is the final amount including the principal.

P is the principal amount.

i is the rate of interest per year.

n is the number of years invested.

anonymous · Answer

what about the 1000 per year deposited?

anonymous · Answer

5000x4 + 1000x3 +
1000x 2 + 1000x + 2500

anonymous · Answer

$11,199.35

anonymous · Answer

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