To determine the total value of the investment after 20 years with an interest rate of 7%, we need to decide whether the interest is simple or compound. I'll calculate both scenarios for you.

1. Simple Interest

The formula for simple interest is:

$A = P(1 + rt)$

Where:

• $A$ is the final amount
• $P$ is the principal amount ($5,000)
• $r$ is the annual interest rate (7%, or 0.07)
• $t$ is the time in years (20 years)

Plugging in the values:

$A = 5000(1 + 0.07 \times 20)$

$A = 5000(1 + 1.4)$

$A = 5000 \times 2.4 = 12000$

So, the total value with simple interest after 20 years would be $12,000.

2. Compound Interest

If the interest is compounded annually, the formula is:

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

Where:

• $A$ is the final amount
• $P$ is the principal amount ($5,000)
• $r$ is the annual interest rate (7%, or 0.07)
• $n$ is the number of times the interest is compounded per year (since we are compounding annually, $n = 1$)
• $t$ is the time in years (20 years)

Plugging in the values:

$A = 5000 \left(1 + \frac{0.07}{1}\right)^{1 \times 20}$

$A = 5000 \times (1.07)^{20}$

$A \approx 5000 \times 3.8697$

$A \approx 19,348.50$

So, the total value with compound interest after 20 years would be $19,348.50.

Would you like more details or have any questions?

Here are 5 related questions:

1. How does the total amount change if the interest is compounded quarterly instead of annually?
2. What would be the total value if the investment period was 10 years instead of 20 years?
3. How much interest is earned with compound interest compared to simple interest over the same period?
4. How would the total amount change if the interest rate was 5% instead of 7%?
5. What would be the total value if $1,000 was added to the investment every year?

Tip: Compound interest significantly increases the investment value over time, especially with longer investment periods and higher compounding frequencies.