The problem on the screen involves calculating the future value and interest earned for an investment with compounded interest. Here is a breakdown of how to approach it:

The Bryants invest $2,500 for 3 years in an account that has an annual interest rate of 1.25% compounded quarterly.

(a) To calculate the future value after 3 years:

The formula for compound interest is:

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

Where:

• $A$ is the future value of the investment (what we're solving for),
• $P = 2500$ is the principal (initial investment),
• $r = 0.0125$ is the annual interest rate (1.25% expressed as a decimal),
• $n = 4$ is the number of times the interest is compounded per year (quarterly),
• $t = 3$ is the number of years.

Now, I'll calculate this for you.The future value of the Bryants' investment after 3 years, assuming no withdrawals are made, is approximately $2,595.38.

(b) To calculate the interest earned:

The interest earned is the difference between the future value and the initial investment:

$\text{Interest} = A - P$

Let me calculate that for you now.The interest earned on the Bryants' investment after 3 years is approximately $95.38.

Summary:

• (a) Total amount in the account after 3 years: $2,595.38
• (b) Interest earned after 3 years: $95.38

Do you have any questions or would you like further details?

Here are 5 related questions for practice:

1. What would the future value be if the interest rate was 2% compounded quarterly?
2. How much interest would be earned if the investment period was 5 years instead of 3 years?
3. What is the future value if the investment is compounded monthly instead of quarterly?
4. How does changing the compounding frequency affect the total interest earned?
5. If the Bryants withdraw $500 after 1 year, how would that impact the future value?

Tip: The more frequently interest is compounded, the more interest you'll earn over time!