The Mitchells are saving up to go on a family vacation in 2 years. They invest $2800 into an account with an annual interest rate of 1.11% compounded monthly. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. ? (a) Assuming no withdrawals are made, how much money is in the Mitchells' account after 2 years? $0 How much interest is earned on the Mitchells' investment after 2 years? S (b) X BA
The Mitchells are saving up to go on a family vacation in 2 years. They invest $2800 into an account with an annual interest rate of 1.11% compounded monthly. Answer the questions below. Do not round any intermediate computations, and round your final answers to the nearest cent. If necessary, refer to the list of financial formulas. ? (a) Assuming no withdrawals are made, how much money is in the Mitchells' account after 2 years? $0 How much interest is earned on the Mitchells' investment after 2 years? S (b) X BA
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
Related questions
Question
Kk.153.
.
**Explanation:**
To solve these problems, you should use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (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.
**Steps for Calculating (a):**
1. Convert the annual interest rate from a percentage to a decimal by dividing by 100.
2. Use the compound interest formula with \( P = 2800 \), \( r = 0.0111 \), \( n = 12 \), and \( t = 2 \).
**Steps for Calculating (b):**
1. Subtract the initial principal from the amount calculated in step (a) to find the interest earned.
**Visual Aids:**
- Provides a compound interest diagram to illustrate the formula and how the interest accumulates over time.
- Interactive calculator tool for students to input values and see real-time results for various principal amounts, interest rates, and periods.
These details ensure the student understands the problem setup, the method to solve it, and can visualize the concepts for better understanding.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F816cc47c-f059-4914-940d-8196a7c7af6b%2F12113002-eb94-482c-b2c6-d3ec59c9b8d8%2Fudf9o5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
The Mitchells are saving up to go on a family vacation in 2 years. They invest $2800 into an account with an annual interest rate of 1.11% compounded monthly.
**Questions:**
1. Assuming no withdrawals are made, how much money is in the Mitchells' account after 2 years?
- Answer: $_____
2. How much interest is earned on the Mitchells' investment after 2 years?
- Answer: $_____
**Instructions:**
- Answer the questions below.
- Do not round any intermediate computations.
- Round your final answers to the nearest cent.
- If necessary, refer to the [list of financial formulas](#).
**Explanation:**
To solve these problems, you should use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount (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.
**Steps for Calculating (a):**
1. Convert the annual interest rate from a percentage to a decimal by dividing by 100.
2. Use the compound interest formula with \( P = 2800 \), \( r = 0.0111 \), \( n = 12 \), and \( t = 2 \).
**Steps for Calculating (b):**
1. Subtract the initial principal from the amount calculated in step (a) to find the interest earned.
**Visual Aids:**
- Provides a compound interest diagram to illustrate the formula and how the interest accumulates over time.
- Interactive calculator tool for students to input values and see real-time results for various principal amounts, interest rates, and periods.
These details ensure the student understands the problem setup, the method to solve it, and can visualize the concepts for better understanding.
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