You want to save up $11,500 to purchase a used car in 4 years. Your account earns an annual rate of 5.1% compounded monthly. How much do you need to deposit each month to meet your goal? Round your answer to two decimal places. Do not include the $ sign in your answer. Your Answer:
You want to save up $11,500 to purchase a used car in 4 years. Your account earns an annual rate of 5.1% compounded monthly. How much do you need to deposit each month to meet your goal? Round your answer to two decimal places. Do not include the $ sign in your answer. Your Answer:
Chapter9: Sequences, Probability And Counting Theory
Section9.4: Series And Their Notations
Problem 62SE: Rachael deposits $1500 into a retirement fund each year. The fund earns 8.2% annual interest,...
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Question
![**Problem Statement:**
You want to save up $11,500 to purchase a used car in 4 years. Your account earns an annual rate of 5.1% compounded monthly. How much do you need to deposit each month to meet your goal?
Round your answer to two decimal places. Do not include the $ sign in your answer.
**Your Answer:**
[Text Box for Answer]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dcfdb23-ad25-456a-a15b-6b05085eda70%2F889a8361-c2ab-4b71-8585-59c235b7d55b%2F5oms5vr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
You want to save up $11,500 to purchase a used car in 4 years. Your account earns an annual rate of 5.1% compounded monthly. How much do you need to deposit each month to meet your goal?
Round your answer to two decimal places. Do not include the $ sign in your answer.
**Your Answer:**
[Text Box for Answer]
![### Investment Problem
**Scenario:**
You wish to deposit $200 each month over the next 20 years into an account that has an annual interest rate of 6.4%, compounded monthly.
**Question:**
How much is in the account at the end of 20 years?
**Instructions:**
Round your answer to two decimal places. Do not include the $ sign in your answer.
**Your Answer:**
[Input box for answer]
### Explanation
To solve this problem, use the future value of an annuity formula, which calculates the future balance of a series of equal payments at regular intervals, compounded at a specific rate.
\[ FV = P \times \frac{{(1 + r/n)^{nt} - 1}}{{r/n}} \]
Where:
- \( P \) is the monthly deposit ($200)
- \( r \) is the annual interest rate (0.064)
- \( n \) is the number of times the interest is compounded per year (12)
- \( t \) is the total number of years (20)
This calculation will give you the total amount in the account after 20 years.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5dcfdb23-ad25-456a-a15b-6b05085eda70%2F889a8361-c2ab-4b71-8585-59c235b7d55b%2Fe0fwjzc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Investment Problem
**Scenario:**
You wish to deposit $200 each month over the next 20 years into an account that has an annual interest rate of 6.4%, compounded monthly.
**Question:**
How much is in the account at the end of 20 years?
**Instructions:**
Round your answer to two decimal places. Do not include the $ sign in your answer.
**Your Answer:**
[Input box for answer]
### Explanation
To solve this problem, use the future value of an annuity formula, which calculates the future balance of a series of equal payments at regular intervals, compounded at a specific rate.
\[ FV = P \times \frac{{(1 + r/n)^{nt} - 1}}{{r/n}} \]
Where:
- \( P \) is the monthly deposit ($200)
- \( r \) is the annual interest rate (0.064)
- \( n \) is the number of times the interest is compounded per year (12)
- \( t \) is the total number of years (20)
This calculation will give you the total amount in the account after 20 years.
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