Question

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Each year, starting on his 12th birthday, James made a deposit into a bank account to save up for a car. On his 12th, 13th, and 14th birthdays, he deposited $750. On his 15th birthday, he deposited $900. On his 16th birthday, he deposited $1200. There were no additional deposits or withdrawals. The bank account earns an annual interest rate of r.

Answer 1

(a)
12th birthday: $750
13th birthday: $750 + $750r
14th birthday: $750 + ($750 + $750r)r
15th birthday: $900 + ($750 + ($750 + $750r)r)r
16th birthday: $1200 + ($900 + ($750 + ($750 + $750r)r)r)r

Polynomial:
$750r^4 + $750r^3 + $750r^2 + $900r + $1200

in terms of x where r = x - 1
$750(x - 1)^4 + $750(x - 1)^3 + $750(x - 1)^2 + $900(x - 1) + $1200

750x^4 - 2250x^3 + 3000x^2 - 1350x + 1050

(b)
if r = 2.8%
$750r^4 + $750r^3 + $750r^2 + $900r + $1200
$750(1.028)^4 + $750(1.028)^3 + $750(1.028)^2 + $900(1.028) + $1200

$4,570.16