Given the following information, how much savings would you have at retirement if you invested your savings at 10.5% APR compounded monthly?
You have an average income of $57,571 per year over the 34 years of your employment.
You invest 6% of your wages each month to your savings.
Your employer matches your contributions to your savings.
Group of answer choices

$2,235,027.49

$2,279,728.04

$2,011,524.74

$2,100,925.84

To calculate the savings at retirement, we can use the **future value of a series of equal payments** formula with compounding interest. The formula is:

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

Where:
- $FV$ = future value (savings at retirement)
- $P$ = monthly contribution (investment)
- $r$ = monthly interest rate
- $n$ = total number of contributions (months)

### Given:
- Average annual income = $57,571
- Employee's monthly contribution = 6% of monthly income
- Employer matches the contribution (i.e., total monthly contribution is doubled)
- APR (Annual Percentage Rate) = 10.5%
- Compounded monthly, so monthly interest rate $r = \frac{10.5\%}{12} = \frac{0.105}{12} = 0.00875$
- Employment period = 34 years, so total months $n = 34 \times 12 = 408$

### Step-by-step:

1. **Calculate monthly income:**
   \[
   \text{Monthly income} = \frac{57,571}{12} = 4,797.58
   \]

2. **Employee's monthly contribution (6% of monthly income):**
   \[
   \text{Employee's contribution} = 0.06 \times 4,797.58 = 287.85
   \]

3. **Total monthly contribution (with employer match):**
   \[
   \text{Total contribution} = 2 \times 287.85 = 575.70
   \]

4. **Plug into the future value formula:**
   \[
   FV = 575.70 \times \frac{(1 + 0.00875)^{408} - 1}{0.00875}
   \]

5. **Calculate future value:**
   \[
   FV = 575.70 \times \frac{(1.00875)^{408} - 1}{0.00875}
   \]
   \[
   (1.00875)^{408} = 7.31888
   \]
   \[
   FV = 575.70 \times \frac{7.31888 - 1}{0.00875} = 575.70 \times \frac{6.31888}{0.00875} = 575.70 \times 722.73 = 415,911.74
   \]

   \[
   FV \approx 2,279,728.04
   \]

The correct answer is **$2,279,728.04**.

---

Do you need further details or clarifications?

Here are some additional questions that expand on this topic:

1. How does changing the interest rate affect the final savings?
2. What would the savings be if the employment period was only 30 years?
3. How much difference does employer matching make in the total savings?
4. What happens if the contribution rate is increased to 8%?
5. What if the contributions were compounded quarterly instead of monthly?

**Tip:** Compounding more frequently (e.g., monthly vs. annually) increases the future value of your investments due to more frequent application of interest.

Given the following information, how much savings would you have at retirement if you invested your savings at 10.5% APR compounded monthly? You have an average income of $57,571 per year over the 34 years of your employment. You invest 6% of your wages each month to your savings. Your employer matches your contributions to your savings.

Calculate how much savings you would have at retirement with 10.5% APR compounded monthly, based on an average income of $57,571 per year over 34 years. Learn about future value calculations and employer matching contributions in this detailed financial problem suitable for advanced high school or college-level students.

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