1. You win the lottery and get $1,000,000. You decide that you want to invest all of the money in a  savings account for 5 years. A bank representative offers you two different savings plans. 
Plan 1-The bank gives you a 6% interest rate and compounds the interest each month. Plan 2- The bank gives you a 12% interest rate and compounds the interest each month. 
A) How much money will you have at the end of the 5 years in plan 1? Round to the nearest cent.  Show all your work.  


To solve this problem, we will use the formula for compound interest:

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

Where:
- $A$ is the amount of money accumulated after interest.
- $P$ is the principal amount (initial investment).
- $r$ is the annual interest rate (in decimal form).
- $n$ is the number of times the interest is compounded per year.
- $t$ is the time the money is invested (in years).

### Plan 1 Calculation

For Plan 1, we are given:
- $P = 1,000,000$ (the initial amount).
- $r = 6\%$ or $0.06$ (the annual interest rate).
- $n = 12$ (since interest is compounded monthly).
- $t = 5$ years.

Now, substituting these values into the compound interest formula:

\[
A = 1,000,000 \left(1 + \frac{0.06}{12}\right)^{12 \times 5}
\]

Let's compute this step by step.

1. Compute the monthly interest rate: $\frac{0.06}{12} = 0.005$.
2. Multiply $n$ and $t$: $12 \times 5 = 60$.
3. Calculate the total factor inside the parentheses: $1 + 0.005 = 1.005$.
4. Raise this factor to the power of 60: $(1.005)^{60}$.
5. Multiply by the principal amount.

I’ll calculate the final result.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can guide you through the process of calculating it manually or using a calculator:

1. Compute the monthly interest rate: $\frac{0.06}{12} = 0.005$.
2. Multiply $n$ and $t$: $12 \times 5 = 60$.
3. Calculate the total factor: $1.005^{60} = 1.34885$.
4. Multiply by the principal: $1,000,000 \times 1.34885 = 1,348,850$.

So, the total amount at the end of 5 years is approximately **$1,348,850**.

Let me know if you need more details, or if you have any questions! Here are 5 related questions:

1. How does compound interest differ from simple interest?
2. What effect does increasing the interest rate have on total interest?
3. How does the frequency of compounding affect the final amount?
4. How would the result change if the interest was compounded annually instead of monthly?
5. What is the formula for calculating continuous compounding interest?

**Tip**: The more frequently interest is compounded, the more interest you will earn!

You win the lottery and get $1,000,000. You decide that you want to invest all of the money in a savings account for 5 years. A bank representative offers you two different savings plans. Plan 1-The bank gives you a 6% interest rate and compounds the interest each month. Plan 2- The bank gives you a 12% interest rate and compounds the interest each month. A) How much money will you have at the end of the 5 years in plan 1? Round to the nearest cent. Show all your work.

Learn how to calculate the final amount when investing $1,000,000 with a 6% monthly compounded interest rate over 5 years. This problem covers key concepts like compound interest and exponents. Suitable for high school students in Grades 9-12.

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