Question

Laura retired from her job recently, and she has saved about $414,731.00 over the course of her career. She plans to withdraw $2,224.00 each month to pay for living expenses. After a certain amount of time, the balance in Laura's account is $381,371.00. How many months have passed since Laura retired

Answer 1

Answer:

15 months.

Step-by-step explanation:

Given:

Laura retired and saved about $414,731.00 over the course of her career.

She plans to withdraw $2,224.00 each month to pay for living expenses.

After a certain amount of time, the balance in Laura's account is $381,371.00

Question asked:

How many months have passed since Laura retired ?

Solution:

Let total number of months for which she withdrew = $x$

Total saving amount = $414,731

Unitary method:

In 1 month she withdrew =  $2,224

In $x$ months she withdrew = $\ 2224x$

Total withdrew amount =  $\ 2224x$

Balance amount after $x$ months = $381,371

Balance amount = Total saving amount - Total withdrew amount

$381371=414731-2224x\\ \\ Subtracting\ both\ sides\ by\ 414731\\ \\ 381371-414731=414731-414731-2224x\\ \\- 33360=-2224x\\ \\ Minus\ canceled\ by\ minus\\ \\ 33360=2224x\\ \\ Dividing\ both\ sides\ by\ 2224\\ \\ \frac{33360}{2224} =\frac{2224x}{2224} \\ \\ 15=x$

Thus, 15 months have passed since Laura retired.