Investigation 1: You plan to invest $1,250 for 7 years. One option is an account paying simple interest at an annual
rate of 2.07%. A second option is a certificate of deposit, or CD, at your bank, which gives a higher interest rate, but
you cannot access your investment for a specified length of time. The CD pays 5.36% annual interest, compounded
monthly. Find the amount you would have in each account after 7 years.
a) First plug in the values into each formula and write them below, then use Excel to calculate the results.

### Step-by-Step Calculation for Each Option:

#### 1. **Simple Interest Formula**:
The formula for simple interest is:

\[
A = P(1 + rt)
\]

where:
- $ A $ is the amount after interest,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years.

For the simple interest account:
- $ P = 1,250 $
- $ r = 0.0207 $ (2.07% as a decimal)
- $ t = 7 $ years

\[
A = 1,250(1 + (0.0207 \times 7)) = 1,250(1 + 0.1449) = 1,250 \times 1.1449
\]

#### 2. **Compound Interest Formula**:
The formula for compound interest is:

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

where:
- $ A $ is the amount after interest,
- $ P $ is the principal amount (initial investment),
- $ r $ is the annual interest rate (as a decimal),
- $ t $ is the time in years,
- $ n $ is the number of times the interest is compounded per year.

For the CD with monthly compounding:
- $ P = 1,250 $
- $ r = 0.0536 $ (5.36% as a decimal)
- $ t = 7 $ years
- $ n = 12 $ (compounded monthly)

\[
A = 1,250 \left(1 + \frac{0.0536}{12}\right)^{12 \times 7} = 1,250 \left(1 + 0.0044667\right)^{84} = 1,250 \times (1.0044667)^{84}
\]

### Excel Calculations:
- **For Simple Interest**:
  Enter the formula in Excel:  
  `=1250*(1+0.0207*7)`  
  This will give you the final amount for the simple interest account.
  
- **For Compound Interest**:
  Enter the formula in Excel:  
  `=1250*(1+(0.0536/12))^(12*7)`  
  This will give you the final amount for the compounded interest in the CD account.

Would you like to go into more detail or verify specific parts of the solution?

### 5 Follow-up Questions:
1. What happens if you change the interest rate for simple interest?
2. How would the result change if the compounding frequency in the CD were quarterly?
3. What is the effect of doubling the investment period to 14 years for both options?
4. How would your results differ if interest was compounded annually instead of monthly?
5. What is the advantage of compound interest over simple interest over long periods?

**Tip**: Compound interest grows faster because you're earning interest on both your initial principal and the interest that has already been added!

Investigation 1: You plan to invest $1,250 for 7 years. One option is an account paying simple interest at an annual rate of 2.07%. A second option is a certificate of deposit, or CD, at your bank, which gives a higher interest rate, but you cannot access your investment for a specified length of time. The CD pays 5.36% annual interest, compounded monthly. Find the amount you would have in each account after 7 years.

Explore how to calculate the final amount for a $1,250 investment over 7 years using both simple and compound interest. Learn the differences between simple interest at 2.07% and monthly compounded interest at 5.36%. Detailed formulas and Excel steps provided. Ideal for students in Grades 9-12.

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