19. Diana put $8000 in a 10-year CD paying 5% interest compounded monthly. After 2 years, she withdrew all her money, and as an early withdrawal penalty, she paid back all the interest she made during the first year. How much money was Diana left with?
19. Diana put $8000 in a 10-year CD paying 5% interest compounded monthly. After 2 years, she withdrew all her money, and as an early withdrawal penalty, she paid back all the interest she made during the first year. How much money was Diana left with?
Algebra and Trigonometry (6th Edition)
6th Edition
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,...
Related questions
Question
![**Problem 19: Early Withdrawal from a Certificate of Deposit (CD)**
Diana invested $8,000 in a 10-year Certificate of Deposit (CD) that offered an annual interest rate of 5%, compounded monthly. After 2 years, Diana decided to withdraw all of her money. Due to an early withdrawal penalty, she had to pay back all the interest she earned during the first year. We need to calculate how much money Diana was left with after these conditions.
**Concepts Involved:**
- Compound Interest
- Early Withdrawal Penalty
**Steps to Solve:**
1. **Calculate the amount accumulated in the CD after 2 years with monthly compounding:**
The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
Given:
- \( P = $8,000 \)
- \( r = 0.05 \)
- \( n = 12 \) (monthly compounding)
- \( t = 2 \) years
Substituting these values into the formula:
\[
A = 8000 \left(1 + \frac{0.05}{12}\right)^{12 \times 2}
\]
2. **Calculate the amount of interest earned after 2 years:**
- First, find the value of \( A \):
\[
A = 8000 \left(1 + 0.0041667\right)^{24} \approx 8000 \left(1.10494\right) \approx 8839.52
\]
3. **Calculate the amount accumulated in the CD after 1 year to determine the interest that must be paid back due to the early withdrawal penalty:**
Given:
- \( P = $8,000 \)
- \( r = 0.05 \)
- \( n =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9168bf64-9e72-49b9-9a77-a0f13a9541a3%2F330f47ea-c7c6-409b-a787-7d27eb64d727%2Fou4ggq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 19: Early Withdrawal from a Certificate of Deposit (CD)**
Diana invested $8,000 in a 10-year Certificate of Deposit (CD) that offered an annual interest rate of 5%, compounded monthly. After 2 years, Diana decided to withdraw all of her money. Due to an early withdrawal penalty, she had to pay back all the interest she earned during the first year. We need to calculate how much money Diana was left with after these conditions.
**Concepts Involved:**
- Compound Interest
- Early Withdrawal Penalty
**Steps to Solve:**
1. **Calculate the amount accumulated in the CD after 2 years with monthly compounding:**
The formula for compound interest is:
\[
A = P \left(1 + \frac{r}{n}\right)^{nt}
\]
where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (the initial amount of money).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time the money is invested for in years.
Given:
- \( P = $8,000 \)
- \( r = 0.05 \)
- \( n = 12 \) (monthly compounding)
- \( t = 2 \) years
Substituting these values into the formula:
\[
A = 8000 \left(1 + \frac{0.05}{12}\right)^{12 \times 2}
\]
2. **Calculate the amount of interest earned after 2 years:**
- First, find the value of \( A \):
\[
A = 8000 \left(1 + 0.0041667\right)^{24} \approx 8000 \left(1.10494\right) \approx 8839.52
\]
3. **Calculate the amount accumulated in the CD after 1 year to determine the interest that must be paid back due to the early withdrawal penalty:**
Given:
- \( P = $8,000 \)
- \( r = 0.05 \)
- \( n =
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education