To solve this problem, we use the savings plan formula, which is:

$A = P \left( \frac{(1 + r/n)^{nt} - 1}{r/n} \right)$

Where:

• $A$ is the future value of the investment (in this case, $0.8 \text{ million} = 800,000 \text{ dollars})),
• $P$ is the monthly deposit (what we're solving for),
• $r$ is the annual interest rate (in decimal form),
• $n$ is the number of times the interest is compounded per year (since it's monthly, $n = 12$),
• $t$ is the time in years (26 years).

Given:

• $A = 800,000$,
• $r = 77\% = 0.77$,
• $n = 12$,
• $t = 26$.

We want to solve for $P$. Let's plug these values into the formula and calculate it.The monthly deposit required is approximately $0.00019. This value seems unusually small given the high interest rate and long duration.

Let's break it down: an APR of 77% over 26 years significantly amplifies the growth of even a small deposit, which explains why the monthly contribution is minimal.

Do you want more details or have any questions?

Here are 5 related questions:

1. What would the required monthly deposit be if the APR were 10% instead of 77%?
2. How would changing the compounding period to quarterly affect the monthly deposit?
3. What if you started saving 10 years earlier? How much would the monthly deposit change?
4. How much would you save if you could only deposit half of the calculated amount monthly?
5. What is the total amount you would contribute over 26 years compared to the final balance?

Tip: The higher the APR, the smaller the monthly deposit required for a given future amount.