80°F Clear Q Set up the formula to find the balance after 8 years for a total of $12,000 invested at an annual interest rate of 9% compounded daily. O A = 12000e(0.09) (8) A = 12000e (9) (8) O O A = 12000 (1 + 2 O A = 12000 (1+) (3 365 S 3 365) (8) (9) E 0.09 (365) (8) $ R F % 5 T G Search A Y H & 7 U * 8 1 F10 ( 9 K O ) 0 L F12 P & Prt Sc { Insert Backspace 1 Ente
80°F Clear Q Set up the formula to find the balance after 8 years for a total of $12,000 invested at an annual interest rate of 9% compounded daily. O A = 12000e(0.09) (8) A = 12000e (9) (8) O O A = 12000 (1 + 2 O A = 12000 (1+) (3 365 S 3 365) (8) (9) E 0.09 (365) (8) $ R F % 5 T G Search A Y H & 7 U * 8 1 F10 ( 9 K O ) 0 L F12 P & Prt Sc { Insert Backspace 1 Ente
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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![### Compound Interest Formula Setup
To determine the final balance after 8 years for an initial investment of $12,000 with an annual interest rate of 9% compounded daily, you need to use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Here:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial amount of money), which is $12,000.
- \( r \) is the annual interest rate (decimal), which is 0.09.
- \( n \) is the number of times that interest is compounded per year, which is 365 for daily compounding.
- \( t \) is the time the money is invested for, which is 8 years.
Given these parameters, the correct formula to find the balance after 8 years is:
\[ A = 12000 \left(1 + \frac{0.09}{365}\right)^{8 \cdot 365} \]
### Multiple-Choice Options:
The options given to select the correct formula are:
1. \( A = 12000e^{(0.09)(8)} \)
2. \( A = 12000e^{(9)(8)} \)
3. \( A = 12000 \left(1 + \frac{9}{365}\right)^{(8)(9)} \)
4. \( A = 12000 \left(1 + \frac{0.09}{365}\right)^{(8)(365)} \)
Among these options, the correct one matches our manually derived formula, which is:
\[ A = 12000 \left(1 + \frac{0.09}{365}\right)^{(8)(365)} \]
Thus, option 4 is the correct answer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7f1ba715-f989-45d9-9496-7979ba76ee2a%2Fcf83c801-2e7a-4152-9435-22605445f704%2Fgtw266w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Compound Interest Formula Setup
To determine the final balance after 8 years for an initial investment of $12,000 with an annual interest rate of 9% compounded daily, you need to use the formula for compound interest:
\[ A = P \left(1 + \frac{r}{n}\right)^{nt} \]
Here:
- \( A \) is the amount of money accumulated after \( n \) years, including interest.
- \( P \) is the principal amount (the initial amount of money), which is $12,000.
- \( r \) is the annual interest rate (decimal), which is 0.09.
- \( n \) is the number of times that interest is compounded per year, which is 365 for daily compounding.
- \( t \) is the time the money is invested for, which is 8 years.
Given these parameters, the correct formula to find the balance after 8 years is:
\[ A = 12000 \left(1 + \frac{0.09}{365}\right)^{8 \cdot 365} \]
### Multiple-Choice Options:
The options given to select the correct formula are:
1. \( A = 12000e^{(0.09)(8)} \)
2. \( A = 12000e^{(9)(8)} \)
3. \( A = 12000 \left(1 + \frac{9}{365}\right)^{(8)(9)} \)
4. \( A = 12000 \left(1 + \frac{0.09}{365}\right)^{(8)(365)} \)
Among these options, the correct one matches our manually derived formula, which is:
\[ A = 12000 \left(1 + \frac{0.09}{365}\right)^{(8)(365)} \]
Thus, option 4 is the correct answer.
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