To solve this problem, we can use the future value of a series formula for compound interest when payments are made periodically. This formula is:

$FV = P \times \frac{(1 + r/n)^{nt} - 1}{r/n}$

Where:

• $FV$ is the future value (the amount in the account after 25 years),
• $P$ is the monthly deposit ($400),
• $r$ is the annual interest rate (7% or 0.07),
• $n$ is the number of times interest is compounded per year (12 times, monthly),
• $t$ is the number of years (25 years).

Plugging in the values:

• $P = 400$
• $r = 0.07$
• $n = 12$
• $t = 25$

$FV = 400 \times \frac{(1 + 0.07/12)^{12 \times 25} - 1}{0.07/12}$

Let me calculate that for you. Given values P = 400 # Monthly deposit r = 0.07 # Annual interest rate n = 12 # Compounded monthly t = 25 # Number of years

Future value formula

FV = P * ((1 + r/n)**(n*t) - 1) / (r/n) FVThe amount in the account after 25 years will be approximately $324,028.68.

Would you like a more detailed breakdown of how the calculation was done? Or do you have any other questions?

Here are some related questions:

1. How does changing the interest rate affect the future value of the deposit?
2. What would happen if the deposit was made annually instead of monthly?
3. How can we calculate the amount in an account if withdrawals are made instead of deposits?
4. What is the difference between simple and compound interest in this case?
5. How can I adjust the formula if the interest is compounded daily or quarterly?

Tip: The more frequently interest is compounded, the higher the future value will be.