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 calculate the amount of money you'll have at the end of 5 years with Plan 1, we will use the formula for compound interest:

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

Where:
- $A$ = the future value of the investment (what we're solving for)
- $P$ = the principal amount (initial investment) = $1,000,000
- $r$ = the annual interest rate = 6% = 0.06
- $n$ = the number of times the interest is compounded per year = 12 (since it's compounded monthly)
- $t$ = the time in years = 5

Now, plug the values into the formula:

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

Simplifying:

\[
A = 1,000,000 \left(1 + 0.005\right)^{60}
\]

\[
A = 1,000,000 \left(1.005\right)^{60}
\]

Now, calculate $1.005^{60}$:

\[
1.005^{60} \approx 1.34885
\]

Finally, multiply by 1,000,000:

\[
A \approx 1,000,000 \times 1.34885 = 1,348,850
\]

So, at the end of 5 years, you will have approximately **$1,348,850.00** in Plan 1.

---

Would you like to explore Plan 2 or need more details? 

Here are 5 related questions to further explore:
1. What would happen if the interest was compounded quarterly instead of monthly?
2. How much would you have with a 10-year investment period in Plan 1?
3. How does the interest rate affect the growth of your savings?
4. What is the formula for continuously compounded interest, and how does it compare to monthly compounding?
5. If you withdrew some money after 3 years, how would it impact your final balance?

**Tip:** The more frequently interest is compounded, the more you earn, as each compounding period adds to the principal for the next period.

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. 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 future value of $1,000,000 invested at a 6% interest rate with monthly compounding over 5 years. This problem demonstrates the compound interest formula and exponential growth in savings. Suitable for high school students in Grades 10-12.

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