Maria has $50 in a savings account in week 1. She plans on depositing $8
each following week. What will be her account balance after 52 weeks?
To find Maria's account balance after 52 weeks, we can calculate it by adding up the deposits made each week over the course of the year.
Maria starts with $50 in week 1.
In week 2, she deposits an additional $8.
In week 3, she deposits another $8.
This pattern continues for the remaining 50 weeks.
So, to calculate the account balance after 52 weeks, we need to sum up all the deposits made:
Total deposits = $8 + $8 + $8 + ... (50 times)
To find the sum of the deposits, we can use the formula for the sum of an arithmetic series:
Sum = (n/2) * (first term + last term)
Where n is the number of terms in the series.
In this case, n = 50 (since we have 50 deposits) and the first term is $8.
So, the sum of the deposits is:
Sum = (50/2) * (8 + last term)
To find the last term of the series, we can use the formula for the nth term of an arithmetic series:
n th term = first term + (n-1) * common difference
Here, the first term is $8, the common difference is also $8, and the n th term is the last term, which we need to find.
n th term = $8 + (50-1) * $8
Now we can substitute the value of the last term into the sum formula:
Sum = (50/2) * (8 + ($8 + (50-1) * $8))
Simplifying this expression:
Sum = 25 * (8 + $8 + 49 * $8)
Sum = 25 * (8 + 8 + 49 * 8)
Sum = 25 * (16 + 392)
Sum = 25 * 408
Sum = $10,200
Thus, Maria's account balance after 52 weeks will be $10,200.