A bank features a savings account that has an annual percentage rate of r = 5.7% with interest compounded quarterly. Shannon deposits $10,500 into the account. r\ kt The account balance can be modeled by the exponential formula A(t) = a(1+:) , where A is k account value after t years , a is the principal (starting amount), r is the annual percentage rate, k is the number of times each year that the interest is compounded. (A) What values should be used for a, r, and k? a = r = k = (B) How much money will Shannon have in the account in 8 years? Answer = $ Round answer to the nearest penny. (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). r k APY = (1 - 1 + k АРY %. %3D Round answer to 3 decimal places.
A bank features a savings account that has an annual percentage rate of r = 5.7% with interest compounded quarterly. Shannon deposits $10,500 into the account. r\ kt The account balance can be modeled by the exponential formula A(t) = a(1+:) , where A is k account value after t years , a is the principal (starting amount), r is the annual percentage rate, k is the number of times each year that the interest is compounded. (A) What values should be used for a, r, and k? a = r = k = (B) How much money will Shannon have in the account in 8 years? Answer = $ Round answer to the nearest penny. (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). r k APY = (1 - 1 + k АРY %. %3D Round answer to 3 decimal places.
Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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![**Understanding Compounded Interest: A Savings Account Example**
A bank features a savings account that has an annual percentage rate of \( r = 5.7\% \) with interest compounded **quarterly**. Shannon deposits $10,500 into the account.
The account balance can be modeled by the exponential formula:
\[ A(t) = a \left(1 + \frac{r}{k}\right)^{kt} \]
where \( A \) is the account value after \( t \) years, \( a \) is the principal (starting amount), \( r \) is the annual percentage rate, and \( k \) is the number of times each year that the interest is compounded.
### Let's break down each part of the problem:
#### (A) What values should be used for \( a \), \( r \), and \( k \)?
Given:
- \( a \) is the principal: Shannon deposits $10,500, so \( a = \boxed{10500} \).
- \( r \) is the annual percentage rate: The rate given is 5.7%, so \( r = \boxed{0.057} \) (as a decimal).
- \( k \) is the number of times interest is compounded each year: Quarterly compounding means \( k = \boxed{4} \).
#### (B) How much money will Shannon have in the account in 8 years?
Using the formula:
\[ A(t) = a \left(1 + \frac{r}{k}\right)^{kt} \]
Plugging in the values:
- \( a = 10,500 \)
- \( r = 0.057 \)
- \( k = 4 \)
- \( t = 8 \)
\[ A(8) = 10500 \left(1 + \frac{0.057}{4}\right)^{4 \cdot 8} \]
Calculate the result to get the amount Shannon will have in the account in 8 years.
#### Answer = $ \boxed{\phantom{0000}} \]
**Round the answer to the nearest penny.**
#### (C) What is the annual percentage yield (APY) for the savings account?
The APY is the actual or effective annual percentage rate which includes all compounding in the year. It can be calculated using:
\[ APY = \left(1 + \frac{r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F633100ea-0428-4ac9-9895-e60fbf23e986%2F48227bd1-37d6-4a32-a36f-8b2af4b28ee2%2Fe73p96u.png&w=3840&q=75)
Transcribed Image Text:**Understanding Compounded Interest: A Savings Account Example**
A bank features a savings account that has an annual percentage rate of \( r = 5.7\% \) with interest compounded **quarterly**. Shannon deposits $10,500 into the account.
The account balance can be modeled by the exponential formula:
\[ A(t) = a \left(1 + \frac{r}{k}\right)^{kt} \]
where \( A \) is the account value after \( t \) years, \( a \) is the principal (starting amount), \( r \) is the annual percentage rate, and \( k \) is the number of times each year that the interest is compounded.
### Let's break down each part of the problem:
#### (A) What values should be used for \( a \), \( r \), and \( k \)?
Given:
- \( a \) is the principal: Shannon deposits $10,500, so \( a = \boxed{10500} \).
- \( r \) is the annual percentage rate: The rate given is 5.7%, so \( r = \boxed{0.057} \) (as a decimal).
- \( k \) is the number of times interest is compounded each year: Quarterly compounding means \( k = \boxed{4} \).
#### (B) How much money will Shannon have in the account in 8 years?
Using the formula:
\[ A(t) = a \left(1 + \frac{r}{k}\right)^{kt} \]
Plugging in the values:
- \( a = 10,500 \)
- \( r = 0.057 \)
- \( k = 4 \)
- \( t = 8 \)
\[ A(8) = 10500 \left(1 + \frac{0.057}{4}\right)^{4 \cdot 8} \]
Calculate the result to get the amount Shannon will have in the account in 8 years.
#### Answer = $ \boxed{\phantom{0000}} \]
**Round the answer to the nearest penny.**
#### (C) What is the annual percentage yield (APY) for the savings account?
The APY is the actual or effective annual percentage rate which includes all compounding in the year. It can be calculated using:
\[ APY = \left(1 + \frac{r
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