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From the image, here's a breakdown of the question and how to approach it:

### Problem Setup:
The problem explores the effects of starting retirement contributions at different ages to reach a retirement fund target of $1,000,000 by age 65, with a 6% annual interest rate, compounded monthly.

1. **First Scenario (starting at age 25):**
   - Goal: $1,000,000 by age 65.
   - Interest Rate: 6% APR, compounded monthly.
   - Monthly Contribution: Calculated as $502.14.
   - Find total personal contribution by retirement.

2. **Second Scenario (starting at age 45):**
   - Same retirement goal of $1,000,000 by age 65.
   - Monthly Contribution: Calculated as $1,924.94.
   - Find total personal contribution and compare with Scenario 1.

### Solution Steps:
To solve this, use the future value of an annuity formula and the given monthly contributions to compute the total contributions.

1. **Total Personal Contribution (for each scenario)**:
   \[
   \text{Total Contribution} = \text{Monthly Contribution} \times \text{Number of Months}
   \]
   - **Scenario 1 (starting at age 25)**:
     \[
     \text{Total Contribution} = 502.14 \times 480 = 240,915.20
     \]
   - **Scenario 2 (starting at age 45)**:
     \[
     \text{Total Contribution} = 1,924.94 \times 240 = 461,985.60
     \]
   
2. **Additional Contribution Needed for Starting Later**:
   \[
   \text{Difference} = 461,985.60 - 240,915.20 = 221,070.40
   \]

These calculations align with the values entered in the form fields. 

Would you like further clarification on any step or details on related calculations?

### Related Questions
1. How would the monthly contribution change if the APR were 8% instead of 6%?
2. How does increasing the retirement age from 65 to 70 impact monthly contributions?
3. What is the impact on contributions if they are compounded quarterly rather than monthly?
4. How much interest will be earned if contributions start at age 30 instead?
5. What would be the required initial investment (no monthly contributions) to reach $1,000,000 by age 65?

### Tip:
Starting early with smaller contributions allows compound interest to grow your investments significantly, reducing the total out-of-pocket amount needed.

We are considering the effects of starting early or late to save for retirement. Assume that each account considered has an APR of 6% compounded monthly.

Following expert advice, you begin your retirement program as soon as you graduate from college at age 25. You plan to retire at the age of 65. What monthly contributions do you need to make to have a retirement account worth $1,000,000?

What will your total personal contribution be by the time you retire if you start saving after graduation?

Against expert advice, you begin your retirement program at age 45. You plan to retire at the age of 65. What monthly contributions do you need to make to have a retirement account worth $1,000,000?

What will your total personal contribution be by the time you retire if you start saving at age 45?

How much more will you personally contribute by the time you retire if you start saving at age 45 instead of starting right after graduation?

Explore the effects of starting retirement savings at age 25 versus age 45 to reach a retirement fund of $1,000,000 by age 65. This problem involves compound interest calculations at a 6% APR compounded monthly, with a breakdown of required monthly contributions and total personal contributions.

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