Scenario 1. John invests $10,000 in a 3-year CD. The earning is 8% APR compounded monthly. (a) What is the payout when this CD matures? (b) If John wants to double his payout when the 8% APR CD matures, how long should he hold this CD? Solution. CD is a Certificate of Deposit. A CD is a product offered by banks with a premium (higher) interest rate. Once started, the money cannot be withdrawn until the CD matures. Here we have several pieces of information, including the initial investment P= $ interest rate i is % APR, and the term is years. However, the interest is compounded monthly. Therefore, our term lasts for months/year x years months. Furthermore, APR is annual-based; we need to convert it to monthly-based. To do that, we just need to divide the APR by 12, e.g., % APR = %/12 monthly = (fourth decimal point, not in percentage). (a) The payout or future value can be calculated through the formula, F P (1+ i $ ) = $ x (1+ . The interest is F- P = $ (b) To double the payout means our F will be $ P is still = $ and the interest rate is still .We can either start with the formula F = P (1 + i) to derive n, or we can just use the formula n = In (F/ P)/In (1+i) In (F/ P) In ($ )=In (write to the fourth decimal point) = (fourth decimal point) In (1 + i) = In (1 + (write to the sixth decimal point) Therefore n In (F/ P)/In (1+i)= months > years (divided by 12 months/year)
Scenario 1. John invests $10,000 in a 3-year CD. The earning is 8% APR compounded monthly. (a) What is the payout when this CD matures? (b) If John wants to double his payout when the 8% APR CD matures, how long should he hold this CD? Solution. CD is a Certificate of Deposit. A CD is a product offered by banks with a premium (higher) interest rate. Once started, the money cannot be withdrawn until the CD matures. Here we have several pieces of information, including the initial investment P= $ interest rate i is % APR, and the term is years. However, the interest is compounded monthly. Therefore, our term lasts for months/year x years months. Furthermore, APR is annual-based; we need to convert it to monthly-based. To do that, we just need to divide the APR by 12, e.g., % APR = %/12 monthly = (fourth decimal point, not in percentage). (a) The payout or future value can be calculated through the formula, F P (1+ i $ ) = $ x (1+ . The interest is F- P = $ (b) To double the payout means our F will be $ P is still = $ and the interest rate is still .We can either start with the formula F = P (1 + i) to derive n, or we can just use the formula n = In (F/ P)/In (1+i) In (F/ P) In ($ )=In (write to the fourth decimal point) = (fourth decimal point) In (1 + i) = In (1 + (write to the sixth decimal point) Therefore n In (F/ P)/In (1+i)= months > years (divided by 12 months/year)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
A4
Transcribed Image Text:This guided practice covers both Modules 6 and 7, on interest calculation and payment plans. Some scenarios
are for single payments, while others are payment plan applications. Please pay attention to how to read the
scenario to determine what it askes for.
Scenario 1. John invests $10,000 in a 3-year CD. The earning is 8% APR compounded monthly. (a) What is the
payout when this CD matures? (b) If John wants to double his payout when the 8% APR CD matures, how long
should he hold this CD?
Solution. CD is a Certificate of Deposit. A CD is a product offered by banks with a premium (higher) interest
rate. Once started, the money cannot be withdrawn until the CD matures.
Here we have several pieces of information, including the initial investment P = $
interest rate i is
% APR, and the term is
years.
However, the interest is compounded monthly. Therefore, our term lasts for
months/year x
years =
months. Furthermore, APR is
annual-based; we need to convert it to monthly-based. To do that, we just need to divide the APR by 12, e.g.,
% APR =
%/12 monthly=
(fourth decimal point, not in percentage).
(a) The payout or future value can be calculated through the formula, F = P (1 + i)n = $
x ((1 +
) = $
. The interest is F - P = $
(b) To double the payout means our F will be $
P is still = $
and the interest rate is still
We can either start with
the formula F = P (1 + i)" to derive n, or we can just use the formula n = In (F/ P)/ In (1+i)
In (F/ P) In ($
)=In
(write to the fourth decimal point) =
(fourth decimal point)
In (1 + i) = In (1 +
(write to the sixth decimal point)
Therefore n = In (F / P)/In (1+i) =
months =>
years (divided by 12 months/year)
![Scenario 2. This question is designed to help you have a better idea of how Plan 2 in Table 4-1 work. Now our
principal is $15,000, the interest rate is 2% per month, and the term is 5 months. Please develop a plan 2 and
answer the following questions.
Solution. Plan 2 is a fixed payment plan, meaning we will pay the same amount at the end of the next five
months. Before developing the payment plan in the plan 2 format, we need to find the monthly payment. In
Excel, we can type in " = pmt (rate, nper, pv, [fv], [type]), where rate =
%, nper =
, and pv =
.We can get pmt = .
(second decimal point).
This value in Excel, depending on the sign of your PV, will either be a positive or negative one. A negative one
only means that it is out of our pocket. But when we put this value into plan 2, we need to use a positive value.
Once we have the payment info, we can start developing the payment plan. There will be five rows in our
plan, representing five periods. For the payment column, all five cells have the same amount. If you are not
familiar with the development of plan 2, I encourage you to review the Excel video in Module 7.
Answer the following questions based on your plan 2:
• The interest due for the first month is $
, and the principal paid is $
• The amount owed at the beginning of month 2 is $
, and the amount owed at
the end of month 2 is $
• The amount of principal paid at the end of month 4 is $
and it is $
for the last month;
• If we add the interest accrued in these five months together, the sum is $](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc541b931-ed61-4d49-baa7-c070b3f98219%2Faada0d21-c12e-4dee-b061-5d12260bb164%2Fy7fnnpd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Scenario 2. This question is designed to help you have a better idea of how Plan 2 in Table 4-1 work. Now our
principal is $15,000, the interest rate is 2% per month, and the term is 5 months. Please develop a plan 2 and
answer the following questions.
Solution. Plan 2 is a fixed payment plan, meaning we will pay the same amount at the end of the next five
months. Before developing the payment plan in the plan 2 format, we need to find the monthly payment. In
Excel, we can type in " = pmt (rate, nper, pv, [fv], [type]), where rate =
%, nper =
, and pv =
.We can get pmt = .
(second decimal point).
This value in Excel, depending on the sign of your PV, will either be a positive or negative one. A negative one
only means that it is out of our pocket. But when we put this value into plan 2, we need to use a positive value.
Once we have the payment info, we can start developing the payment plan. There will be five rows in our
plan, representing five periods. For the payment column, all five cells have the same amount. If you are not
familiar with the development of plan 2, I encourage you to review the Excel video in Module 7.
Answer the following questions based on your plan 2:
• The interest due for the first month is $
, and the principal paid is $
• The amount owed at the beginning of month 2 is $
, and the amount owed at
the end of month 2 is $
• The amount of principal paid at the end of month 4 is $
and it is $
for the last month;
• If we add the interest accrued in these five months together, the sum is $
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, finance and related others by exploring similar questions and additional content below.Recommended textbooks for you
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Essentials Of Investments
Finance
ISBN:
9781260013924
Author:
Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:
Mcgraw-hill Education,
Foundations Of Finance
Finance
ISBN:
9780134897264
Author:
KEOWN, Arthur J., Martin, John D., PETTY, J. William
Publisher:
Pearson,
Fundamentals of Financial Management (MindTap Cou…
Finance
ISBN:
9781337395250
Author:
Eugene F. Brigham, Joel F. Houston
Publisher:
Cengage Learning
Corporate Finance (The Mcgraw-hill/Irwin Series i…
Finance
ISBN:
9780077861759
Author:
Stephen A. Ross Franco Modigliani Professor of Financial Economics Professor, Randolph W Westerfield Robert R. Dockson Deans Chair in Bus. Admin., Jeffrey Jaffe, Bradford D Jordan Professor
Publisher:
McGraw-Hill Education