To determine how much interest Frank's account will earn after 2 years with a 5% interest rate compounded annually, we use the compound interest formula:

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

Where:

• $A$ is the amount of money in the account after $t$ years (including interest).
• $P$ is the principal (initial deposit), which is $4,000.
• $r$ is the annual interest rate (5% or 0.05).
• $n$ is the number of times the interest is compounded per year (since it's compounded annually, $n = 1$).
• $t$ is the time the money is invested (2 years in this case).

Substituting the values:

$A = 4000 \left(1 + \frac{0.05}{1}\right)^{1 \times 2} = 4000 (1.05)^2$

First, we calculate $(1.05)^2$:

$1.05^2 = 1.1025$

Now, multiply by the principal:

$A = 4000 \times 1.1025 = 4410$

The amount in the account after 2 years will be $4,410. To find the interest earned, subtract the initial deposit from the final amount:

$\text{Interest} = 4410 - 4000 = 410$

So, the account will earn $410 in interest after 2 years.

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What if Frank deposited $4,000 at a 7% interest rate compounded annually?
2. How much interest would Frank earn in 5 years instead of 2?
3. What if the interest was compounded quarterly instead of annually?
4. What would be the total amount if Frank withdrew $500 after 1 year?
5. How would the interest differ if the rate was 5% compounded monthly?

Tip: The more frequently interest is compounded, the more interest you will earn, as the interest is calculated more often.