Question

Phalicia is a senior at North HS and wants to begin saving for college. She's trying to choose between two savings account options.

Option 1: Phalicia deposits $300 and deposits an additional $50 each month.
Option 2: Phalicia deposits $5 and it triples each month.
Which option should she choose

Answer 1

Option 2

Explanation:

Let's say that Phalicia opens her savings account one year (12 months) before she goes to college.

With Option 1, she would have saved 300 + 50 * 11 = $850. We do 50 * 11 and not 50 * 12 because she deposits $50 for 11 months, not 12.

With Option 2, she would have saved 5 * 3¹¹ = $885735. Note that we do 3¹¹ and not 3¹² because 5 is being tripled 11 times.

Obviously, she should choose Option 2 because she saves A LOT more money.

Additionally, we can notice that Option 1 is an example of an arithmetic sequence whereas Option 2 is an example of a geometric sequence. Their explicit formulas would be aₙ = 50n + 250 and aₙ = 5 * 3⁽ⁿ⁻¹⁾ respectively.