To calculate the amount of money you will have in the account after 10 years with Option 1, which offers 6.5% interest per year, compounded quarterly, we'll 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 interest.
• $P$ is the initial principal (in this case, $5000).
• $r$ is the annual interest rate (6.5% or 0.065 as a decimal).
• $n$ is the number of times the interest is compounded per year (quarterly means $n = 4$).
• $t$ is the number of years the money is invested (in this case, 10 years).

Step 1: Substitute the known values into the formula:

$A = 5000 \left(1 + \frac{0.065}{4}\right)^{4 \times 10}$

Step 2: Simplify the expression inside the parentheses:

= 5000 \left(1 + 0.01625\right)^{40} = 5000 \left(1.01625\right)^{40}$$ ### Step 3: Calculate $$(1.01625)^{40}$$: $$1.01625^{40} \approx 1.87347$$ ### Step 4: Multiply by the principal: $$A = 5000 \times 1.87347 \approx 9367.35$$ So, the amount of money in your account after 10 years with Option 1 is approximately **$9367.35**. --- Would you like further details or have any questions? Here are 5 related questions to deepen your understanding: 1. What would be the outcome if the interest rate was 5% instead of 6.5%? 2. How does the number of compounding periods affect the total amount? 3. What would happen if you invested for 15 years instead of 10? 4. How does quarterly compounding compare to monthly compounding at the same rate? 5. How does the formula change if the interest rate is compounded annually? **Tip:** Always double-check the number of compounding periods per year when using the compound interest formula, as it significantly affects the final amount.