To calculate the future value (FV) of an investment, you can use the formula for compound interest:

$FV = P \times (1 + r)^t$

Where:

• $P$ = Principal (initial deposit) = $3,800
• $r$ = annual interest rate = 7% = 0.07
• $t$ = time in years

Part 1: Value after 30 years

Using the formula for 30 years: $FV = 3800 \times (1 + 0.07)^{30}$

Let's calculate:

$FV = 3800 \times (1.07)^{30}$ $FV = 3800 \times 7.612255$ $FV \approx 28,926.57$

So, after 30 years, your account would be worth $28,926.57.

Part 2: Value after 35 years

Using the formula for 35 years: $FV = 3800 \times (1 + 0.07)^{35}$

Let's calculate:

$FV = 3800 \times (1.07)^{35}$ $FV = 3800 \times 8.349574$ $FV \approx 31,732.78$

So, after 35 years, your account would be worth $31,732.78.

Summary:

• After 30 years, the account will be worth $28,926.57.
• After 35 years, the account will be worth $31,732.78.

Would you like more details or further clarification on any of the steps?

Here are five related questions for you:

1. How does changing the interest rate affect the future value?
2. What would happen to the account value if you added monthly contributions?
3. How would the future value change if the investment period was only 20 years instead of 30 or 35 years?
4. Can you explain the effect of compounding frequency on future value (e.g., annually, quarterly, monthly)?
5. What are the steps to solve for the present value if you know the future value?

Tip: The longer you leave your money in an account with compound interest, the more it benefits from the "compounding effect," meaning the interest earned gets added to the principal and also earns interest over time.