A passbook savings account has a rate of 8%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year. iClick the icon to view some finance formulas. The effective annual yield is %. (Round to the nearest tenth as needed.)
A passbook savings account has a rate of 8%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year. iClick the icon to view some finance formulas. The effective annual yield is %. (Round to the nearest tenth as needed.)
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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![**Problem Statement:**
A passbook savings account has a rate of 8%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year.
---
(Information Icon) Click the icon to view some finance formulas.
---
The effective annual yield is [ ]%.
*(Round to the nearest tenth as needed.)*
---
**Explanation for Educators:**
The problem requires calculating the effective annual yield (EAY) with the given nominal rate and compounding frequency. The formula for EAY is:
\[ \text{EAY} = \left(1 + \frac{r}{n}\right)^n - 1 \]
where \( r \) is the nominal annual interest rate (0.08 for 8%) and \( n \) is the number of compounding periods per year (1000 in this case).
To solve:
1. Substitute the values into the formula.
2. Calculate the expression.
3. Convert to a percentage by multiplying by 100.
4. Round the result to the nearest tenth as required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e7854b-0be5-41c7-9658-968f15b06285%2F5f8e6dd0-c779-4ccb-b033-a234138b6172%2F32ak2ai_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A passbook savings account has a rate of 8%. Find the effective annual yield, rounded to the nearest tenth of a percent, if the interest is compounded 1000 times per year.
---
(Information Icon) Click the icon to view some finance formulas.
---
The effective annual yield is [ ]%.
*(Round to the nearest tenth as needed.)*
---
**Explanation for Educators:**
The problem requires calculating the effective annual yield (EAY) with the given nominal rate and compounding frequency. The formula for EAY is:
\[ \text{EAY} = \left(1 + \frac{r}{n}\right)^n - 1 \]
where \( r \) is the nominal annual interest rate (0.08 for 8%) and \( n \) is the number of compounding periods per year (1000 in this case).
To solve:
1. Substitute the values into the formula.
2. Calculate the expression.
3. Convert to a percentage by multiplying by 100.
4. Round the result to the nearest tenth as required.
![In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form.
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]
\[
A = Pe^{rt}
\]
\[
Y = \left(1 + \frac{r}{n}\right)^{n} - 1
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7e7854b-0be5-41c7-9658-968f15b06285%2F5f8e6dd0-c779-4ccb-b033-a234138b6172%2F48q0iu9_processed.png&w=3840&q=75)
Transcribed Image Text:In the provided formulas, A is the balance in the account after t years, P is the principal investment, r is the annual interest rate in decimal form, n is the number of compounding periods per year, and Y is the investment's effective annual yield in decimal form.
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
\[
P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}}
\]
\[
A = Pe^{rt}
\]
\[
Y = \left(1 + \frac{r}{n}\right)^{n} - 1
\]
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