Retirement Funding.  Barry has just become eligible for his​ employer-sponsored retirement plan. Barry is 35 and plans to retire at 65. Barry calculates that he can contribute ​$4 comma 600 per year to his plan.​ Barry's employer will match this amount. If Barry can earn a return of 6​% on his​ investment, he will have ​$727 comma 335 at retirement. Assuming a return of 6​%, how much would Barry have if he could invest an additional ​$880 per year that his employer would match beginning at age 35​?
Part 2
If Barry could invest an additional ​$880 per year that his employer would match beginning at age 35​, at​ retirement, he would have ​$

enter your response here.  ​(Round to the nearest​ dollar.)

To calculate how much Barry would have at retirement if he could invest an additional $880 per year, which his employer would also match, we need to find the future value of an annuity. 

Here is the step-by-step calculation:

1. **Determine the total annual contribution:**
   - Barry's initial contribution: $4,600
   - Employer's match: $4,600
   - Additional contribution: $880
   - Employer's match on additional contribution: $880
   - Total annual contribution = $4,600 + $4,600 + $880 + $880 = $10,960

2. **Calculate the future value of the annuity:**
   - Annual contribution (PMT): $10,960
   - Annual interest rate (r): 6% or 0.06
   - Number of years (n): 65 - 35 = 30

The future value of an annuity formula is:
\[ FV = PMT \times \frac{(1 + r)^n - 1}{r} \]

3. **Substitute the values into the formula:**
\[ FV = 10,960 \times \frac{(1 + 0.06)^{30} - 1}{0.06} \]

4. **Calculate the components:**
\[ (1 + 0.06)^{30} = 5.74349 \] (approximately)
\[ \frac{5.74349 - 1}{0.06} = \frac{4.74349}{0.06} = 79.0582 \]

5. **Calculate the future value:**
\[ FV = 10,960 \times 79.0582 = 866,736 \] (approximately)

Therefore, if Barry could invest an additional $880 per year that his employer would match, at retirement he would have approximately $866,736.

### Summary
If Barry could invest an additional $880 per year that his employer would match beginning at age 35, at retirement, he would have approximately **$866,736**.

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Would you like details on any specific part of the calculation, or do you have any other questions?

Here are some related questions you might want to explore:
1. How is the future value of an annuity calculated?
2. What if the annual return rate was different?
3. How does compound interest affect retirement savings?
4. What other factors should be considered in retirement planning?
5. How can Barry's contributions change over time to increase retirement savings?

**Tip:** Always ensure to revisit and potentially revise your retirement contributions periodically, especially if your income increases or your financial goals change.

Explore how Barry can maximize his retirement savings by calculating the impact of an additional $880 annual investment matched by his employer. Learn the step-by-step process using the Future Value of Annuity formula with a 6% annual return rate. Estimate Barry's retirement savings with accurate financial planning.

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