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: $
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: $
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78db42f9-6d62-48c9-a117-b436e469106b%2F0f07bcd1-410c-439f-bf76-83a91bca40c9%2Fh45wh98_processed.jpeg&w=3840&q=75)
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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