The equation is y = x + 35.275.
Step-by-step explanation:
Step 1; Gizmo starts at $425 and the monthly rate of return is 8.3%. So every month he gets back 8.3% of the $425 he starts with. To calculate how much 8.3% of $425 is we make 8.3% a fraction by dividing it by 100 and multiplying it with the amount.
8.3% of $425 = [tex]\frac{8.3}{100}[/tex] × $425 = 0.083 × $425 = $35.275.
So every month $35.275 is added to the balance of the account.
Step 2; Assume y is the amount of money in the account at the end of the month while x is the amount of money at the end of the previous month's end. Using x and y we can form the following equation,
y = x + 35.275.
For the first month, y = x + 35.725 = 425 + 35.725 = $460.725.
For the second month, y = x + 35.725 = 460.725 + 35.725 = $496.45.
For the third month, y = x + 35.725 = 496.45 + 35.725 = $532.175.
For the fourth month, y = x + 35.725 = 532.175 + 35.725 = $567.90.
For the fifth month, y = x + 35.725 = 567.90 + 35.725 = $603.625.
For the sixth month, y = x + 35.725 = 603.625 + 35.725 = $639.35.
For the seventh month, y = x + 35.725 = 639.35 + 35.725 = $675.075.
For the eighth month, y = x + 35.725 = 675.075 + 35.725 = $710.80.
For the ninth month, y = x + 35.725 = 710.80 + 35.725 = $746.525.
For the tenth month, y = x + 35.725 = 746.525 + 35.725 = $782.25.
For the eleventh month,y = x + 35.725 = 782.25 + 35.725 = $817.975.
For the twelfth month, y = x + 35.725 = 817.975 + 35.725 = $853.70
Gizmo then adds $250 to the $853.70 at the beginning of the second year.
