What is the total amount you will have at the end of the investment? - $


(b) How much of your retirement savings will have come from your total contributions? (This should include your initial balance if there is one). - $


(c) How much of your retirement savings will have come from interest (growth)?


 (Answer these questions using this information: Current age: 19

Age you plan to retire: 50

About how much money do you currently have in investments? Enter 0 if necessary. - $0

How much will you contribute monthly - $100)


To calculate the total amount you will have at the end of the investment, the portion of your retirement savings from contributions, and the portion from interest (growth), we need to use the **future value of a series** formula for monthly contributions.

The formula is:

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

Where:
- $ FV $ = future value (total amount at retirement)
- $ P $ = monthly contribution
- $ r $ = monthly interest rate (annual interest rate divided by 12)
- $ n $ = total number of months (investment period in years multiplied by 12)

Now, let’s break it down:

### Given Information:
- **Current age**: 19
- **Retirement age**: 50
- **Investment period**: 50 - 19 = 31 years
- **Monthly contribution**: $100
- **Current balance**: $0
- We need to assume an average annual interest rate (let's assume 7% as a typical stock market return, which is common for long-term retirement investments).

1. **Interest rate** ($r$):
   - Annual interest rate: 7% or 0.07
   - Monthly interest rate: $ r = \frac{0.07}{12} = 0.005833 $ (about 0.583%)

2. **Total number of months** ($n$):
   - $ n = 31 \times 12 = 372 $ months

Now, let's calculate the future value and answer the questions:

### (a) **Total amount at retirement**:
Using the formula for future value of a series:
\[
FV = 100 \times \left( \frac{(1 + 0.005833)^{372} - 1}{0.005833} \right) \times (1 + 0.005833)
\]

Let me calculate this for you.### (a) **Total amount at retirement**:
The total amount you will have at retirement is approximately **$132,825.86**.

### (b) **Amount from contributions**:
To calculate how much of this total comes from your contributions, simply multiply your monthly contribution by the total number of months:

\[
\text{Total contributions} = P \times n = 100 \times 372 = 37,200
\]

So, the total amount coming from your contributions will be **$37,200**.

### (c) **Amount from interest (growth)**:
The amount coming from interest (growth) is the difference between the total amount at retirement and the contributions:

\[
\text{Interest (growth)} = FV - \text{Total contributions} = 132,825.86 - 37,200 = 95,625.86
\]

So, the amount from interest (growth) will be approximately **$95,625.86**.

---

### Summary:
- **Total amount at retirement**: $132,825.86
- **From contributions**: $37,200
- **From interest (growth)**: $95,625.86

Would you like any more details or clarifications? Here are some related questions:

1. What if the interest rate was lower, say 5%?
2. How would the total change if you started contributing earlier or later?
3. What if you increased your monthly contribution to $200?
4. How would inflation affect the value of your retirement savings?
5. Can you withdraw your retirement funds early without penalties?

**Tip**: The earlier you start saving, the more you benefit from compound interest!

What is the total amount you will have at the end of the investment? (b) How much of your retirement savings will have come from your total contributions? (This should include your initial balance if there is one). (c) How much of your retirement savings will have come from interest (growth)? (Answer these questions using this information: Current age: 19, Age you plan to retire: 50, About how much money do you currently have in investments? Enter 0 if necessary. - $0, How much will you contribute monthly - $100)

Learn how to calculate your retirement savings with monthly contributions of $100 over 31 years, from age 19 to 50, using the compound interest formula. Explore how much of your total savings will come from contributions and interest growth, assuming a 7% annual return. Suitable for Grades 10-12.

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