Assuming you want to have $500,000, how much money would you need to deposit each month for 75 years at 2% in order to have $500,000 in your account at the beginning of retirement?
Round to the nearest cent.

To find out how much money you need to deposit each month to reach $500,000 at the end of 75 years, given an interest rate of 2% per year, we can use the formula for the future value of an ordinary annuity:

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

Where:
- $ FV $ is the future value ($500,000),
- $ P $ is the monthly payment (which we're solving for),
- $ r $ is the monthly interest rate (annual rate divided by 12),
- $ n $ is the total number of payments (75 years × 12 months/year).

### Step 1: Break down the variables
- $ FV = 500,000 $
- $ r = \frac{2\%}{12} = 0.02 / 12 = 0.00166667 $ (monthly interest rate),
- $ n = 75 \times 12 = 900 $ (total number of months).

### Step 2: Solve for $ P $
We can rearrange the formula to solve for $ P $:

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

Let me calculate the exact amount you need to deposit each month.The monthly deposit you would need to make is approximately **$239.73** in order to accumulate $500,000 over 75 years at an annual interest rate of 2%.

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. How does changing the interest rate affect the monthly deposit required?
2. What if you deposit a lump sum at the beginning instead of monthly deposits?
3. How would inflation impact the value of $500,000 in 75 years?
4. What if you want to reach $1,000,000 in the same period with the same interest rate?
5. How does compound interest work in different investment vehicles?

**Tip**: Even small increases in interest rates can have a large impact on long-term savings due to compounding effects.

Assuming you want to have $500,000, how much money would you need to deposit each month for 75 years at 2% in order to have $500,000 in your account at the beginning of retirement?

Learn how to calculate the monthly deposit needed to accumulate $500,000 over 75 years with a 2% annual interest rate. Using the future value annuity formula, this problem demonstrates how compound interest and consistent savings can help you reach your financial goals. Suitable for Grades 11-12.

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