Question

Derrick’s parents are finalizing a budget for his college expenses. His first year of college will cost $8,000, and his expenses will increase by 12% each year. What is the amount they should budget for Derrick’s four-year college education, to the nearest dollar?

$38,235 is needed.
$42,823 is needed.
$32,072 is needed.
$39,200 is needed.

Answer 1

$38,235 is needed.

Explanation:

Given,

The cost of first year of college is $ 8000 and it is increasing by 12 % each year,

So, His first year's cost = $ 8000,

Second year's cost = 12 % more than the first year's cost = 112 % of first year's cost = 112 % of 8000 = 1.12 × 8000 = $ 8960,

Third year's cost = 112 % of second year's cost = 112 % of 8960 = 1.12 × 8960 = $ 10035.2

Fourth year's cost = 112% of third year's cost = 1.12 × 10035.2 = $ 11239.424

Hence, Total cost for four-year college education = 8000 + 8960 + 10035.2 + 11239.424 = $ 38234.624 ≈ $ 38235

⇒ $38,235 is needed.

Answer 2

1st year = 8000

2nd year = 8000 * 1.12 = 8960

3rd year = 8960*1.12 = 10035.20

4th year = 10035.20 * 1.12 = 11239.42

8000 + 8960 + 10035.20 + 11239.42 = 38234.62 round to $38,235