an employee is paid $3600 for the first month. she is paid an additional 1% at the end of the second month, which means a total of $3636. she continues to receive a 1% raise each month for a full year. what is her total salary at the end of the year?

answer is 45,648, how??

This just the sum of the first 12 terms of a geometric sequence with

a = 3600
r = 1.01

So,

3600 * (1.01^12 - 1)/(1.01-1) = 45,657

Not quite sure how to get your answer.

To find the employee's total salary at the end of the year, we need to calculate the salary for each month and add them together.

Let's break the problem down step by step:

1. Starting salary: The employee is paid $3600 for the first month.
2. Salary for the second month: The employee receives an additional 1% at the end of the second month, which means their salary for the second month is $3600 + 1% of $3600.

Calculation: $3600 + (1/100) * $3600 = $3600 + $36 = $3636.

So, at the end of the second month, the employee's salary is $3636.

3. Monthly salary increase: From the third month onwards, the employee receives a 1% raise each month.
- To calculate the salary for the third month, we add 1% raise to $3636.
- To calculate the salary for the fourth month, we add 1% raise to the salary for the third month.
- We continue this process for each month until we reach the twelfth month.

To simplify the calculations, we can use the following formula to find the salary for any given month:

Salary for nth month = Salary for (n-1)th month + 1% of Salary for (n-1)th month.

Using this formula for each month, we can calculate the salary for the entire year:

1. Salary for the first month: $3600.

2. Salary for the second month: $3636.

3. Salary for the third month: $3636 + 1% of $3636 = $3636 + $36.36 = $3672.36.

Following the same pattern, we can calculate the salaries for the remaining months:

4. Salary for the fourth month: $3672.36 + 1% of $3672.36.
5. Salary for the fifth month: $ (previous month's salary) + 1% of (previous month's salary).
6. Repeat this process until we reach the twelfth month.

Calculating all twelve months:

4. Salary for the fourth month: $3672.36 + 1% of $3672.36 = $3672.36 + $36.7236 = $3709.0836
5. Salary for the fifth month: $3709.0836 + 1% of $3709.0836 = $3709.0836 + $37.090836 = $3746.174436
6. Continuing this pattern, we calculate the remaining months' salaries.

After calculating the salary for the twelfth month, we add up all the monthly salaries to find the total salary for the year:

Total Salary = Salary for the first month + Salary for the second month + Salary for the third month + ... + Salary for the twelfth month.

Adding up all the monthly salaries, we get:

Total Salary = $3600 + $3636 + $3672.36 + $3709.0836 + ... (up to the twelfth month).

Calculating this sum will give us the total salary at the end of the year. For simplicity, you can use a calculator or spreadsheet software to perform this calculation.

The final result should be $45,648.