What lump sum do parents need to deposit in an account earning 6%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 10 years? (Round your answer to the nearest cent.)
What lump sum do parents need to deposit in an account earning 6%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 10 years? (Round your answer to the nearest cent.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![### Educational Content: Compound Interest Calculation
**Problem Statement:**
What lump sum do parents need to deposit in an account earning 6%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 10 years? (Round your answer to the nearest cent.)
**Solution Guide:**
To solve this problem, you will 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 deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
In this scenario:
- \( A = 100,000 \)
- \( r = 0.06 \)
- \( n = 12 \) (monthly compounding)
- \( t = 10 \)
**Instructions:**
- Substitute the given values into the formula to solve for \( P \).
- Rearrange the formula to find \( P \):
\[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \]
- Calculate the result and round to the nearest cent.
### Conclusion:
By following the steps above, you will determine the exact lump sum required to reach the savings goal in 10 years. Consider using a calculator for precision.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe8dbb38b-67db-4869-a2fb-b3f37c286b0c%2F916eb51f-65fa-4257-957f-1a2706194a62%2Fpc8claj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content: Compound Interest Calculation
**Problem Statement:**
What lump sum do parents need to deposit in an account earning 6%, compounded monthly, so that it will grow to $100,000 for their son's college fund in 10 years? (Round your answer to the nearest cent.)
**Solution Guide:**
To solve this problem, you will 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 deposit).
- \( r \) is the annual interest rate (decimal).
- \( n \) is the number of times that interest is compounded per year.
- \( t \) is the time in years.
In this scenario:
- \( A = 100,000 \)
- \( r = 0.06 \)
- \( n = 12 \) (monthly compounding)
- \( t = 10 \)
**Instructions:**
- Substitute the given values into the formula to solve for \( P \).
- Rearrange the formula to find \( P \):
\[ P = \frac{A}{\left(1 + \frac{r}{n}\right)^{nt}} \]
- Calculate the result and round to the nearest cent.
### Conclusion:
By following the steps above, you will determine the exact lump sum required to reach the savings goal in 10 years. Consider using a calculator for precision.
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