Solve the following real-world problem: destiny opens a checking account with $100 and then deposits $27 each week. How many weeks will it take for her account to reach $343?
Options:
3.16 weeks
9 weeks
16.4 weeks
12.7 weeks
To solve this problem, we can use the formula for the future value of a series of equal deposits:
FV = P * ((1 + r)^n - 1) / r
Here, P is the amount of each deposit ($27), r is the interest rate (which we assume to be 0 since it is not mentioned in the problem), FV is the future value we want to achieve ($343), and n is the number of deposits, which is what we need to find.
Plugging in the given values into the formula, we get:
343 = 27 * ((1 + 0)^n - 1) / 0
Simplifying the equation, we have:
343 = 27 * (1^n - 1) / 0
343 * 0 = 27 * (1^n - 1)
0 = 27 * (1^n - 1)
Since any number raised to the power of 0 equals 1, we can simplify the equation further:
0 = 27 * (1 - 1)
0 = 27 * 0
The equation 0 = 27 * 0 is satisfied, which means that the account balance will reach $343 after 0 weeks.
Therefore, the correct option is not listed among the given options.