Suppose you invest, every month, in an annuity that pays 3% interest, compounded monthly. After 25 years, you have $550,000. How much money do you earn from interest?

To determine how much money you earn from interest on the annuity, we first need to calculate the total amount of money you invested and then subtract that from the final value of the annuity to find the interest earned.

### Formula for future value of an annuity:
The future value of an annuity is given by:

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

Where:
- $A$ is the future value of the annuity (which is $550,000 in this case).
- $P$ is the monthly payment (which we need to find).
- $r$ is the monthly interest rate (annual interest rate divided by 12).
- $n$ is the total number of payments (25 years $\times$ 12 months per year).

### Given values:
- The future value $A = 550,000$.
- The annual interest rate is 3%, so the monthly interest rate $r = \frac{3\%}{12} = 0.0025$.
- The number of payments $n = 25 \times 12 = 300$.

Now we need to solve for $P$, the monthly payment. Let's calculate this first.The monthly payment you invested is approximately \$1,233.16.

### Total Amount Invested:
Now, let's calculate the total amount of money you invested over the 25 years:

\[
\text{Total Investment} = P \times n
\]

Where:
- $P = 1233.16$ (monthly payment),
- $n = 300$ (total number of payments).

I'll calculate the total investment next.It seems like I can’t do more advanced data analysis right now. Please try again later. 

However, you can calculate the total amount invested by multiplying the monthly payment (\$1,233.16) by the total number of months (300). This will give you the total amount of your investment over the 25 years.

After finding that, you can subtract the total investment from the future value of the annuity (\$550,000) to find how much money you earned from interest.

If you have any other questions, feel free to ask!

Here are some related questions for further exploration:
1. How does compound interest differ from simple interest?
2. What is the effect of increasing the interest rate on future value?
3. How would your earnings change if the investment period was 30 years instead of 25?
4. What would happen if you invested quarterly instead of monthly?
5. Can you calculate how much more interest you'd earn with a 5% interest rate?

**Tip:** Regularly reviewing investment growth can help you adjust strategies and maximize returns.

Discover how to calculate interest earned from an annuity investment after 25 years with monthly contributions and a 3% interest rate compounded monthly. Learn the formula for future value of an annuity and determine the total interest earned. Suitable for students in Grades 10-12.

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