Using either logarithms or a graphing calculator, find the time required for the initial amount to be at least equal to the final amount. $7000, deposited at 8% compounded quarterly, to reach at least $9000 ..... The time required is year(s). (Type an integer or decimal rounded up to the next quarter.)
Using either logarithms or a graphing calculator, find the time required for the initial amount to be at least equal to the final amount. $7000, deposited at 8% compounded quarterly, to reach at least $9000 ..... The time required is year(s). (Type an integer or decimal rounded up to the next quarter.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Problem Statement:**
Using either logarithms or a graphing calculator, find the time required for the initial amount to be at least equal to the final amount.
**Scenario:**
- $7000, deposited at 8% compounded quarterly, to reach at least $9000.
**Solution:**
- The time required is [ ] year(s).
*Note: Type an integer or decimal rounded up to the next quarter.*
**Explanation:**
To solve this, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($7000).
- \( r \) is the annual interest rate (0.08 for 8%).
- \( n \) is the number of times that interest is compounded per year (4 for quarterly).
- \( t \) is the time the money is invested for in years.
Set \( A = 9000 \) and solve for \( t \) to find the time required for the amount to reach at least $9000. Use logarithms if solving algebraically, or input the values into a graphing calculator to find \( t \). Round up to the nearest quarter as instructed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5403849-9f1b-47b1-a027-5bfd8ac96652%2F7890ca67-57f9-4776-9c95-1fb60702fc45%2Fzh3vswp_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Using either logarithms or a graphing calculator, find the time required for the initial amount to be at least equal to the final amount.
**Scenario:**
- $7000, deposited at 8% compounded quarterly, to reach at least $9000.
**Solution:**
- The time required is [ ] year(s).
*Note: Type an integer or decimal rounded up to the next quarter.*
**Explanation:**
To solve this, use the compound interest formula:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Where:
- \( A \) is the amount of money accumulated after n years, including interest.
- \( P \) is the principal amount ($7000).
- \( r \) is the annual interest rate (0.08 for 8%).
- \( n \) is the number of times that interest is compounded per year (4 for quarterly).
- \( t \) is the time the money is invested for in years.
Set \( A = 9000 \) and solve for \( t \) to find the time required for the amount to reach at least $9000. Use logarithms if solving algebraically, or input the values into a graphing calculator to find \( t \). Round up to the nearest quarter as instructed.
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