To calculate the total amount accumulated using the compound interest formula, we use the following equation:

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

where:

• $A$ = the total amount accumulated
• $P$ = the principal amount (initial investment)
• $r$ = annual interest rate (decimal)
• $n$ = number of times interest is compounded per year
• $t$ = number of years the money is invested for

Given:

• $P = 9000$
• $r = 0.07$
• $n = 360$
• $t = 2$

Plugging in the values:

$A = 9000 \left(1 + \frac{0.07}{360}\right)^{360 \times 2}$

Now, calculating it step by step:

1. Calculate $\frac{0.07}{360}$: $\frac{0.07}{360} \approx 0.000194444$

2. Calculate $360 \times 2 = 720$.

3. Calculate $\left(1 + 0.000194444\right)^{720}$: $(1.000194444)^{720} \approx 1.148882$

4. Calculate $A$: $A \approx 9000 \times 1.148882 \approx 10339.94$

The total amount accumulated after 2 years is approximately $10,339.94.

Interest Earned

To find the interest earned, subtract the principal from the total amount:

$\text{Interest} = A - P = 10339.94 - 9000 \approx 1339.94$

The interest earned is approximately $1,339.94.

Summary

• Total Amount Accumulated: $10,339.94
• Interest Earned: $1,339.94

Would you like further details or do you have any questions? Here are some related questions you might consider:

1. How would the total amount change if the interest rate were 5% instead of 7%?
2. What would be the total amount if compounded annually instead of daily?
3. How does increasing the investment period affect the total accumulated amount?
4. What is the difference between compound interest and simple interest?
5. How would the results change if the principal amount was $10,000 instead of $9,000?

Tip: Always check the compounding frequency, as it significantly impacts the total amount accumulated.