Charlie has $16,000 to invest for a period of 5 years. The following three alternatives are available to him: • Account 1 pays 3.00 % for year 1.4.00 % for year 2, 6.00% for year 3, 8.00 % for year 4, and 11.00 % for year 5, all with annual compounding. • Account 2 pays 11.00% for year 1, 8.00% for year 2, 6.00% for year 3, 4.00% for year 4, and 3.00% for year 5, all with annual compounding. • Account 3 pays interest at the rate of 6.36154% per year for all 5 years. Based on the available balance at the end of year 5, which alternative is Charlie's best choice? Year 5 Balance, Alternative 1:$ Year 5 Balance, Alternative 2: $ Year 5 Balance, Alternative 3: $

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**Investment Choices Analysis for Charlie**

**Scenario:**

Charlie has $16,000 to invest for a period of 5 years. The following three alternatives are available to him:

**- Account 1** pays:
  - 3.00% for year 1
  - 4.00% for year 2
  - 6.00% for year 3
  - 8.00% for year 4
  - 11.00% for year 5
  - All with annual compounding.

**- Account 2** pays:
  - 11.00% for year 1
  - 8.00% for year 2
  - 6.00% for year 3
  - 4.00% for year 4
  - 3.00% for year 5
  - All with annual compounding.

**- Account 3** pays interest at the rate of 6.36154% per year for all 5 years.
  - With continuous compounding.

**Instructions:**

Based on the available balance at the end of year 5, which alternative is Charlie's best choice?

**Calculation Area:**

- **Year 5 Balance, Alternative 1:**
  - $
- **Year 5 Balance, Alternative 2:**
  - $
- **Year 5 Balance, Alternative 3:**
  - $

---

**Investment Analysis:**

To help Charlie determine the best investment choice, calculate the final balance for each account option after 5 years.

**Steps for Calculation:**

1. **Account 1 and Account 2:**
   - Use the formula for compound interest with annual compounding:
     \[
     A = P \left(1 + \frac{r}{100}\right)^n
     \]
   - Where:
     - \(A\) is the amount of money accumulated after n years, including interest.
     - \(P\) is the principal amount ($16,000).
     - \(r\) is the annual interest rate.
     - \(n\) is the number of years.

2. **Account 3:**
   - Use the formula for continuous compounding:
     \[
     A = Pe^{rt}
     \]
   - Where:
     - \(e\) is the base of the natural logarithm (approximately equal to 2.718
Transcribed Image Text:**Investment Choices Analysis for Charlie** **Scenario:** Charlie has $16,000 to invest for a period of 5 years. The following three alternatives are available to him: **- Account 1** pays: - 3.00% for year 1 - 4.00% for year 2 - 6.00% for year 3 - 8.00% for year 4 - 11.00% for year 5 - All with annual compounding. **- Account 2** pays: - 11.00% for year 1 - 8.00% for year 2 - 6.00% for year 3 - 4.00% for year 4 - 3.00% for year 5 - All with annual compounding. **- Account 3** pays interest at the rate of 6.36154% per year for all 5 years. - With continuous compounding. **Instructions:** Based on the available balance at the end of year 5, which alternative is Charlie's best choice? **Calculation Area:** - **Year 5 Balance, Alternative 1:** - $ - **Year 5 Balance, Alternative 2:** - $ - **Year 5 Balance, Alternative 3:** - $ --- **Investment Analysis:** To help Charlie determine the best investment choice, calculate the final balance for each account option after 5 years. **Steps for Calculation:** 1. **Account 1 and Account 2:** - Use the formula for compound interest with annual compounding: \[ A = P \left(1 + \frac{r}{100}\right)^n \] - Where: - \(A\) is the amount of money accumulated after n years, including interest. - \(P\) is the principal amount ($16,000). - \(r\) is the annual interest rate. - \(n\) is the number of years. 2. **Account 3:** - Use the formula for continuous compounding: \[ A = Pe^{rt} \] - Where: - \(e\) is the base of the natural logarithm (approximately equal to 2.718
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