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.