75. Interest rates Suppose $5000 is invested in a savings account for 10 years (120 months), with an annual interest rate of r, compounded monthly. The amount of money in the account after 10 years is given by A(r) = 5000(1+r/12) ¹20. a. Show there is a value of r in (0, 0.08)-an interest rate between 0% and 8%-that allows you to reach your savings goal of $7000 in 10 years. b. Use a graph to illustrate your explanation in part (a). Then approximate the interest rate required to reach your goal.
75. Interest rates Suppose $5000 is invested in a savings account for 10 years (120 months), with an annual interest rate of r, compounded monthly. The amount of money in the account after 10 years is given by A(r) = 5000(1+r/12) ¹20. a. Show there is a value of r in (0, 0.08)-an interest rate between 0% and 8%-that allows you to reach your savings goal of $7000 in 10 years. b. Use a graph to illustrate your explanation in part (a). Then approximate the interest rate required to reach your goal.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
100%
Answers see given but can’t seem to solve correctly. Please show work, thank you!
![75.10
a. A(r) is continuous on [0, 0.08], and 7000 is between A(0) = 5000
and A(0.08) = 11, 098.20. By the Intermediate Value Theorem,
there is at least one c in (0, 0.08) such that A(c) = 7000.
b. c≈ 0.034 or 3.4%
12,000+
8000-
4000-
0
0.02 0.04
y = 7000
0.06 0.08 0.10 r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F627ffe10-a730-4e4c-b7e9-b306478e5985%2F7b25ac94-0463-4a13-8087-ebdac5dcbeb6%2Fe4u7xnte_processed.jpeg&w=3840&q=75)
Transcribed Image Text:75.10
a. A(r) is continuous on [0, 0.08], and 7000 is between A(0) = 5000
and A(0.08) = 11, 098.20. By the Intermediate Value Theorem,
there is at least one c in (0, 0.08) such that A(c) = 7000.
b. c≈ 0.034 or 3.4%
12,000+
8000-
4000-
0
0.02 0.04
y = 7000
0.06 0.08 0.10 r
Transcribed Image Text:75. Interest rates Suppose $5000 is invested in a savings account for 10
years (120 months), with an annual interest rate of r, compounded monthly.
The amount of money in the account after 10 years is given by
A(r) = 5000(1+r/12) ¹20.
a. Show there is a value of r in (0, 0.08)-an interest rate between 0%
and 8%-that allows you to reach your savings goal of $7000 in 10
years.
b. Use a graph to illustrate your explanation in part (a). Then
approximate the interest rate required to reach your goal.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
