Answer:
2022
Explanation:
The duration of the loan David takes = 20 year loan
The amount David takes as loan = 70,000
The year David takes the loan = 2010
The year/loan balance relationship is y = -98·x² - 1,531·x + 69,710 (We note that the proper constant for the loan balance should be approximately 70,000, therefore the added zero)
Where;
x = The number of yeas
y = The balance
The year his loan balance will be $37,234.7, is given as follows;
37,234.7 = -98·x² - 1,531·x + 69,710
-98·x² - 1,531·x + 69,710 - 37,234.7 = 0
-98·x² - 1,531·x + 32,475.3 = 0
Factorizing with a graphic calculator, gives;
-98·(x - 11.998)·(x + 27.62) = 0
∴ x = 11.998 ≈ 12 or -27.62
The number of years it takes for the loan balance to be $37,234.7 = 12 years
Given that he took the loan in 2010, the loan balance will be $37,234.7 in 2010 + 12 = 2022