Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![### Compound Interest Comparison for Patrick and Brooklyn
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as the principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.
#### Patrick's Account (3% Interest Compounded Quarterly)
Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \)
- \( P = 300 \) (Principal amount)
- \( r = 0.03 \) (Annual interest rate)
- \( n = 4 \) (Number of times interest is compounded per year)
- \( t = 2 \) (Time in years)
\[ A = 300 \left(1 + \frac{0.03}{4}\right)^{4 \times 2} \]
\[ A = 300 \left(1 + 0.0075\right)^8 \]
\[ A = 300 \left(1.0075\right)^8 \]
\[ A = 300 \times 1.06152006 \]
\[ A \approx 318.46 \]
#### Brooklyn's Account (5% Interest Compounded Monthly)
Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \)
- \( P = 300 \) (Principal amount)
- \( r = 0.05 \) (Annual interest rate)
- \( n = 12 \) (Number of times interest is compounded per year)
- \( t = 2 \) (Time in years)
\[ A = 300 \left(1 + \frac{0.05}{12}\right)^{12 \times 2} \]
\[ A = 300 \left(1 + 0.00416667\right)^{24} \]
\[ A = 300 \left(1.00416667\right)^{24} \]
\[ A = 300 \times 1.10494134 \]
\[ A \approx 331.48 \]
#### Conclusion
After 2 years, Patrick's account will have approximately $318.46, while Brooklyn's account will have approximately $331.48. Therefore, Brooklyn's method of depositing](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F355372c0-0b06-4568-8d9a-cddd4364f7ea%2F50732632-1d14-4270-a17a-330a723f542e%2Fc6u33b9_processed.png&w=3840&q=75)
Transcribed Image Text:### Compound Interest Comparison for Patrick and Brooklyn
Patrick and Brooklyn are making decisions about their bank accounts. Patrick wants to deposit $300 as the principal amount, with an interest of 3% compounded quarterly. Brooklyn wants to deposit $300 as the principal amount, with an interest of 5% compounded monthly. Explain which method results in more money after 2 years. Show all work.
#### Patrick's Account (3% Interest Compounded Quarterly)
Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \)
- \( P = 300 \) (Principal amount)
- \( r = 0.03 \) (Annual interest rate)
- \( n = 4 \) (Number of times interest is compounded per year)
- \( t = 2 \) (Time in years)
\[ A = 300 \left(1 + \frac{0.03}{4}\right)^{4 \times 2} \]
\[ A = 300 \left(1 + 0.0075\right)^8 \]
\[ A = 300 \left(1.0075\right)^8 \]
\[ A = 300 \times 1.06152006 \]
\[ A \approx 318.46 \]
#### Brooklyn's Account (5% Interest Compounded Monthly)
Formula: \( A = P \left(1 + \frac{r}{n}\right)^{nt} \)
- \( P = 300 \) (Principal amount)
- \( r = 0.05 \) (Annual interest rate)
- \( n = 12 \) (Number of times interest is compounded per year)
- \( t = 2 \) (Time in years)
\[ A = 300 \left(1 + \frac{0.05}{12}\right)^{12 \times 2} \]
\[ A = 300 \left(1 + 0.00416667\right)^{24} \]
\[ A = 300 \left(1.00416667\right)^{24} \]
\[ A = 300 \times 1.10494134 \]
\[ A \approx 331.48 \]
#### Conclusion
After 2 years, Patrick's account will have approximately $318.46, while Brooklyn's account will have approximately $331.48. Therefore, Brooklyn's method of depositing
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