D Use the compound interest to determine the final Value of the given amonnts i) $ 850 "at sl. compounded daily for 18. yours needod The final Value is $ a Gronnd to mearest cent'as # boo at b%. componnded continously for 10 The final' value is 4 (ronnd to the reavost centas years. heded
D Use the compound interest to determine the final Value of the given amonnts i) $ 850 "at sl. compounded daily for 18. yours needod The final Value is $ a Gronnd to mearest cent'as # boo at b%. componnded continously for 10 The final' value is 4 (ronnd to the reavost centas years. heded
Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Compound Interest Calculation Exercise
Use the compound interest formulas to determine the final value of the given amounts:
#### Problem 1
1. **Initial Amount (Principal):** $850
2. **Interest Rate:** 5% compounded daily
3. **Time Period:** 18 years
**Question:**
What is the final value of $850 at 5% compounded daily for 18 years?
**Solution Expression:**
The final value is $ \_\_\_\_ (rounded to the nearest cent as needed).
#### Problem 2
1. **Initial Amount (Principal):** $800
2. **Interest Rate:** 6% compounded continuously
3. **Time Period:** 10 years
**Question:**
What is the final value of $800 at 6% compounded continuously for 10 years?
**Solution Expression:**
The final value is $ \_\_\_\_ (rounded to the nearest cent as needed).
### Explanation of Compound Interest
- **Daily Compounding:** When interest is compounded daily, the formula used is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( P \) is the principal amount ($850)
- \( r \) is the annual interest rate (5% or 0.05)
- \( n \) is the number of times interest is compounded per year (365 for daily)
- \( t \) is the time the money is invested for in years (18 years)
- \( A \) is the amount of money accumulated after n years, including interest.
- **Continuous Compounding:** When interest is compounded continuously, the formula used is:
\[ A = Pe^{rt} \]
where:
- \( P \) is the principal amount ($800)
- \( r \) is the annual interest rate (6% or 0.06)
- \( t \) is the time the money is invested for in years (10 years)
- \( e \) is the mathematical constant approximately equal to 2.71828
- \( A \) is the amount of money accumulated after n years, including interest.
**Note:** Ensure to round the final answers to the nearest cent as required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbb48b187-83f1-4dc9-80dd-ddef9eb815af%2Fec274ec6-5757-4dee-b68e-e242c1e87598%2Fezro4zd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Compound Interest Calculation Exercise
Use the compound interest formulas to determine the final value of the given amounts:
#### Problem 1
1. **Initial Amount (Principal):** $850
2. **Interest Rate:** 5% compounded daily
3. **Time Period:** 18 years
**Question:**
What is the final value of $850 at 5% compounded daily for 18 years?
**Solution Expression:**
The final value is $ \_\_\_\_ (rounded to the nearest cent as needed).
#### Problem 2
1. **Initial Amount (Principal):** $800
2. **Interest Rate:** 6% compounded continuously
3. **Time Period:** 10 years
**Question:**
What is the final value of $800 at 6% compounded continuously for 10 years?
**Solution Expression:**
The final value is $ \_\_\_\_ (rounded to the nearest cent as needed).
### Explanation of Compound Interest
- **Daily Compounding:** When interest is compounded daily, the formula used is:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
where:
- \( P \) is the principal amount ($850)
- \( r \) is the annual interest rate (5% or 0.05)
- \( n \) is the number of times interest is compounded per year (365 for daily)
- \( t \) is the time the money is invested for in years (18 years)
- \( A \) is the amount of money accumulated after n years, including interest.
- **Continuous Compounding:** When interest is compounded continuously, the formula used is:
\[ A = Pe^{rt} \]
where:
- \( P \) is the principal amount ($800)
- \( r \) is the annual interest rate (6% or 0.06)
- \( t \) is the time the money is invested for in years (10 years)
- \( e \) is the mathematical constant approximately equal to 2.71828
- \( A \) is the amount of money accumulated after n years, including interest.
**Note:** Ensure to round the final answers to the nearest cent as required.
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