You are graduating from college at the end of this semester and have decided to invest 

​$4 comma 5004,500 

at the end of each year into a Roth IRA​ (a retirement investment account that grows tax free and is not taxed when it is​ liquidated) for the next 

4040 

years. If you earn 

55 

percent compounded annually on your investment of 

​$4 comma 5004,500 

at the end of each​ year, how much will you have when you retire in 

4040 

​years? How much will you have if you wait 10 years before beginning to save and only make 

3030 

payments into your retirement​ account?  

Question content area bottom

Part 1

Click on the table icon to view the FVIFA​ table: 

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.

When you retire in 

4040 

​years, you will have 

​$enter your response here. 

 ​(Round to the nearest​ dollar.)

Part 2

If you wait 10 years before beginning to save and only make 

3030 

payments into your retirement​ account, when you retire you will have 

​$enter your response here. 

 ​(Round to the nearest​ dollar.)

### Part 1: Retirement after 40 years of saving

You're making an annual contribution of $4,500 for 40 years, earning a 5% annual return. To calculate how much you'll have at retirement, we can use the **future value of an annuity formula**:

\[
FV = P \times \left( \frac{(1 + r)^n - 1}{r} \right)
\]

Where:
- $P = 4,500$ (annual payment),
- $r = 0.05$ (annual interest rate of 5%),
- $n = 40$ (number of years or contributions).

Substituting the values into the formula:

\[
FV = 4,500 \times \left( \frac{(1 + 0.05)^{40} - 1}{0.05} \right)
\]

Let me calculate that for you.After 40 years of contributing $4,500 annually at a 5% interest rate, you will have approximately **$543,599** when you retire.

---

### Part 2: Retirement after waiting 10 years to start saving

If you wait 10 years to start saving, you'll make only 30 contributions instead of 40. The formula remains the same, but now $n = 30$:

\[
FV = P \times \left( \frac{(1 + r)^{30} - 1}{r} \right)
\]

Let me calculate this for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can use the same formula as in Part 1 for 30 payments. Just substitute $n = 30$ instead of $n = 40$ into the following formula:

\[
FV = 4,500 \times \left( \frac{(1 + 0.05)^{30} - 1}{0.05} \right)
\]

Let me know if you need more assistance! Here are some follow-up questions to expand on this topic:

1. How does compound interest affect long-term investments like Roth IRAs?
2. What is the significance of starting to save early for retirement?
3. How does delaying contributions affect the future value of an annuity?
4. What other factors besides interest rate can impact retirement savings?
5. How can periodic increases in annual contributions enhance retirement savings?

**Tip**: Starting retirement contributions early can significantly boost your savings due to the compounding effect.

You are graduating from college at the end of this semester and have decided to invest $4,500 at the end of each year into a Roth IRA (a retirement investment account that grows tax free and is not taxed when it is liquidated) for the next 40 years. If you earn 5% compounded annually on your investment of $4,500 at the end of each year, how much will you have when you retire in 40 years? How much will you have if you wait 10 years before beginning to save and only make 30 payments into your retirement account?

Discover how to calculate the future value of a Roth IRA with annual contributions of $4,500 over 40 years at 5% interest. Compare with waiting 10 years to begin saving. This financial math problem covers compound interest and future value of an annuity, ideal for college-level students.

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