Question

Fatimah is planning for retirement. Starting May 2014 she puts $250 Fatimah is planning for retirement. Starting May 2014 she puts $250 per month into her retirement account. Each January and July she plans on increasing her monthly contribution by $50. How much will she be putting in per month in September 2024? Responseser month into her retirement account. Each January and July she plans on increasing her monthly contribution by $50. How much will she be putting in per month in September 2024

Answer 1

`\bold{ANSWER:}`
$1150 per month


`\bold{SOLUTION:}`

• To find out how much Fatimah will be putting in per month in September 2024, we need to first determine the pattern of her monthly contributions.

• Starting from May 2014, Fatimah puts $250 per month into her retirement account. Every January and July, she increases her monthly contribution by $50.

Let's break it down step by step:

STEP 1: Identify the months that have a contribution increase:

- January: Starting from January 2015, and every January thereafter, she increases her contribution.

- July: Starting from July 2015, and every July thereafter, she increases her contribution.

STEP 2: Determine the increase in monthly contribution:

- In January, she increases her monthly contribution by $50.

- In July, she increases her monthly contribution by $50.

STEP 3: Calculate the number of increase periods until September 2024:

- The increase periods are from May 2014 to September 2024, excluding the month of September 2024.

Let's count the number of increase periods for January:

- January 2015 to January 2024:

- Number of years: 2024 - 2015 = 9 years.

- Number of increases: 9 • 1 = 9 increases.

- Total increase for January: 9 • 50 = 450

And now the number of increase periods for July:

- July 2015 to July 2024:

- Number of years: 2024 - 2015 = 9 years.

- Number of increases: 9 • 1 = 9 increases.

- Total increase for July: 9 • 50 = 450

4. Calculate the current monthly contribution in September 2024:

- Base monthly contribution: $250.

- Total increase for January: $450.

- Total increase for July: $450.

- Total contribution increase: 450 + 450 = 900

- Current monthly contribution in September 2024: 250 + 900 = $1150

Therefore,

Fatimah will be putting $1150 per month into her retirement account in September 2024.