An account pays interest at a nominal rate of 3% per year. (a) Find the effective annual yield if interest is compounded monthly. Round your answer to three decimal places. % (b) Find the effective annual yield if interest is compounded continuously. Round your answer to three decimal places. % FN.
An account pays interest at a nominal rate of 3% per year. (a) Find the effective annual yield if interest is compounded monthly. Round your answer to three decimal places. % (b) Find the effective annual yield if interest is compounded continuously. Round your answer to three decimal places. % FN.
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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![### Interest Calculation Exercise
#### View Policies
**Current Attempt in Progress**
An account pays interest at a nominal rate of 3% per year.
1. **(a) Find the effective annual yield if interest is compounded monthly.**
Round your answer to three decimal places.
- [Input Box] %
2. **(b) Find the effective annual yield if interest is compounded continuously.**
Round your answer to three decimal places.
- [Input Box] %
**Note:** The input boxes are intended for students to enter their calculated effective annual yields, which will be evaluated based on monthly and continuous compounding methods respectively.
---
#### Explanation:
For (a), you need to use the formula for effective annual yield (EAY) when interest is compounded monthly:
\[ \text{EAY} = \left(1 + \frac{r}{n} \right)^n - 1 \]
where:
- \( r \) is the nominal interest rate (0.03 for 3%)
- \( n \) is the number of compounding periods per year (12 for monthly)
For (b), you need to use the formula for continuous compounding:
\[ \text{EAY} = e^r - 1 \]
where:
- \( r \) is the nominal interest rate (0.03 for 3%)
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828)
Utilize these formulas to calculate and kindly round your results to three decimal places before inputting them in the respective boxes.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F660a15be-f1ca-4f1d-9222-efc14cd423b5%2F6193e8b4-d1bc-4e28-a78c-c783f955a614%2Fr3j3sfa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Interest Calculation Exercise
#### View Policies
**Current Attempt in Progress**
An account pays interest at a nominal rate of 3% per year.
1. **(a) Find the effective annual yield if interest is compounded monthly.**
Round your answer to three decimal places.
- [Input Box] %
2. **(b) Find the effective annual yield if interest is compounded continuously.**
Round your answer to three decimal places.
- [Input Box] %
**Note:** The input boxes are intended for students to enter their calculated effective annual yields, which will be evaluated based on monthly and continuous compounding methods respectively.
---
#### Explanation:
For (a), you need to use the formula for effective annual yield (EAY) when interest is compounded monthly:
\[ \text{EAY} = \left(1 + \frac{r}{n} \right)^n - 1 \]
where:
- \( r \) is the nominal interest rate (0.03 for 3%)
- \( n \) is the number of compounding periods per year (12 for monthly)
For (b), you need to use the formula for continuous compounding:
\[ \text{EAY} = e^r - 1 \]
where:
- \( r \) is the nominal interest rate (0.03 for 3%)
- \( e \) is the base of the natural logarithm (approximately equal to 2.71828)
Utilize these formulas to calculate and kindly round your results to three decimal places before inputting them in the respective boxes.
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