Final answer:
To cover a $12 annual bank fee with a savings account earning 10% interest compounded annually, you would need to deposit $120. This would only break even; it's also recommended to save three to nine months' worth of income for emergency situations.
Step-by-step explanation:
To determine how much money you need in a savings account to start earning and to cover the $12 bank account fee, we need to calculate the amount that will generate at least $12 in interest annually. If the bank offers a 10% interest rate compounded annually, we use the formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested or borrowed for in years. For this case, if you need to earn at least $12 a year to break even on the account fee, we set A to $12, and rearrange the formula to solve for P since we're trying to find the initial deposit needed (P = A / (1 + r/n)^(nt)). Assuming interest is compounded annually (n=1), we find that to earn $12 at a 10% annual interest, the initial deposit (P) should be $120. However, it's also recommended as part of being a responsible adult to have a savings cushion, ideally three to nine months' worth of income. This ensures you have funds for unforeseen situations, like unemployment or major expenses.