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 **compound interest formula**:

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

Where:
- $A$ = the amount of money in the account after $t$ years
- $P$ = the principal (initial amount) = $1,000,000
- $r$ = annual interest rate (as a decimal)
- $n$ = number of times the interest is compounded per year
- $t$ = time the money is invested (in years)

### Plan 1: 6% Interest Rate, Compounded Monthly
Given:
- $P = 1,000,000$
- $r = 6\% = 0.06$
- $n = 12$ (monthly compounding, so 12 times per year)
- $t = 5$ years

Substitute these values into the formula:

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

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

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

Now, let's calculate this.

\[
A = 1,000,000 \times 1.34885
\]

\[
A \approx 1,348,850.97
\]

### Conclusion for Plan 1:
After 5 years, you will have approximately **$1,348,850.97**.

---

Would you like to see the detailed steps for Plan 2 (12% interest rate)? Let me know if you need further clarification or any other questions! Here are some related questions to expand on this:

### Relative Questions:
1. What if the interest compounded quarterly instead of monthly for Plan 1?
2. How much would the total be after 10 years instead of 5 years for Plan 1?
3. What is the difference between compound interest and simple interest in terms of growth?
4. How would the calculation change if the interest was compounded daily?
5. What is the effective annual rate (EAR) for Plan 1 with monthly compounding?

### Tip:
When comparing interest rates, always consider not only the rate itself but also the frequency of compounding, as it significantly impacts the final amount.

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.

Discover how to calculate the final amount of a $1,000,000 investment in a savings account with a 6% annual interest rate, compounded monthly over 5 years. This step-by-step solution uses the compound interest formula, ideal for students in Grades 10-12 or anyone interested in financial math.

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