ACTIVITY BRIEF FOR ASSESSMENT 3
ACADEMIC YEAR 2021 \u2013 2022 – SPRING
Course BCO126 \u2013 Mathematics of Finance (3CH\/4ECTS)
Instructor Florent Vezin
Participation in all assessment activities stated in this document is required. An overall course total of 70
points is required to pass the course. Due dates and times are always in Geneva time.
Assessment 3
Final Assessment Due date and
time
Weight of
course total
Task 3.1: Quiz
Assessment type: Quiz
Description: Student should be able to define annuities and
perpetuities
For further details of this assessment task, please consult the activity
description on the relevant week of the course site.
28\/03\/2022 16:00 8%
Task 3.2: Loan amortization
Assessment type: Written assignment
Description: Student should be able to choose appropriate formula
for given problem
For further details of this assessment task, please consult the activity
description on the relevant week of the course site.
04\/04\/2022 16:00 8%
Main task
Task 3.3: Final assessment
Assessment type: Written assignment
Description: Comprehensive case applying concepts covered during
the course
See sections below for further details.
16\/05\/2022 16:00 24%
INSTRUCTIONS
Main task
The Marco family comprising Mrs. Marco aged 40, Mr. Marco, aged 39, and their three young children
relocated to Barcelona in January 2020 when Mrs. Marco received a job offer from an international firm.
They rented a three-bedroom condominium in Barcelona for 2.100\u20ac per month, which included parking and
fees. While renting made life easy, the Marco family began weighing the pros and cons of purchasing a flat, in
the same building, that became available in June 2020. The idea of home ownership as a form of long-term
investment appealed to the couple. The preliminary rental payments could be used for mortgage payments
instead. While searching for the right property they found a nice apartment at one of the best locations of the
city.
The apartment was owned and had been promoted by a state-owned construction company and was offering
two alternatives:
Option I: renting the apartment with a perpetual contract, meaning forever. The family was very happy living in
that area, and they had the chance to live there forever at an offered price of 1,650 EUR the first month, and
the rent price will be growing by a 0.125% monthly. This option would prevent the Marco family from applying
for a loan, which represented a heavy burden off the family\u2019 budget.
Option II: consisted in acquiring the property with a mortgage scheme for 35 years. The total price of the
apartment is 875.000\u20ac. The family can pay an initial down payment of 275,000 EUR and the rest (600,000
EUR) to be paid in constant monthly payments with an annual interest rate of a 2.75% compounded monthly.
Mrs. Marco establishes the maximum amount they can pay monthly as 2.250\u20ac.
In case of taking option I, what is the amount of the monthly payment the Marco family should pay in 35 years
(in month 420)? (only the amount to be paid that month, show the calculations)
In case of taking option I, how much money will have the Marco family paid in total after 35 years?
If the Marcon family decides to leave Barcelona in 10 years, to attend a better offer elsewhere, what is the
present value of the rental contract offered by the owner as option I? (consider 2.75% compounded monthly
as the interest\/discount rate)
If Mrs. Marco decides to buy the apartment, and accepts Option II, what will be the amount of each monthly
payment to be done during the next 35 years?
Mrs. Marco believes that, if she takes option II and acquires the flat, she might be interested in selling the
apartment in 35 years\u2019 time. If she wants to recover all the money invested (initial payments plus all monthly
payments done), what will be the price she will ask for that apartment at that moment?
Mrs. Marco is happy for knowing how to calculate future values and present values, because this helps in
taking financial decisions. She wonders what the future value of the flat will be in 35 years, if the interest rate
for this type of operations is an annual 1.75% (comp. monthly). Find the Future Value of that apartment in 35
years.
The Marco family thinks that the monthly payments they\u2019ll have to afford during the next thirty five years are
too much, and believes the seller could be convinced about making constant payments only once per year, at
the end of each year. The interest rate would still be the same 2.75% (but now that would be compounded
yearly instead of monthly). What is the amount of the yearly payment to be done?
In this case (yearly payments) what is the total amount the Marco family will have paid in total after 35 years?
(again, just find how much has Mrs. Marconi paid in total)
In this case (yearly payments), how much has the family saved (if any) by paying yearly instead of monthly
installments?
In case that the Marco family pays the pending amount in yearly payments, the owner can only grant them
2.75% interest during the first 10 years. There is the possibility that, after the first 10 years the interest rate
increases to a 3.25% for the remaining 25 years. How much should the Marco family pay per year from year
11 onwards if this occurs?
FORMAT
Your submission must meet the following formatting requirements:
\u2022 Submit one file(s) only.
\u2022 Required file format for main submission: PDF (.pdf)
\u2022 Additional file format for additional deliverables: Not applicable.
\u2022 Additional file requirements: None
Other details:
\u2022 Font size 12
\u2022 Double-spaced
\u2022 Number of words: N\/A
All refencing and citations require Harvard referencing style.
LEARNING OUTCOMES
On successful completion of this assessment, students will be able to:
\u2022 understand the perpetuity and annuity valuation and their factors \u2013 annual and periodical \u2013
and with various starting dates with and without growth;
\u2022 demonstrate an ability to apply the technical skills related to the course in a practical context;
\u2022 assess the future revenue generation of a regular savings scheme and the amount needed
to be saved over time to meet a future series of payments;
\u2022 determine percentage calculations and discounting.
\u2022
ASSESSMENT CRITERIA
Criteria Accomplished
(A)
Proficient (B) Partially
proficient (C)
Borderline (D) Fail (F)
Problem
identification
The student
effectively
identified all the
issues to be solved
and selected all
appropriate
financial formulae
to solve the
problem.
The student
correctly identified
most but not all
issues to be
solved and\/or
selected most but
not all appropriate
financial formulae
to solve the
problem.
The student
correctly
identified most
but not all issues
to be solved but
showed a lack of
understanding in
selecting
appropriate
financial formulae
The students
showed a lack of
fully
understanding
the issues to be
solved and failed
to select
appropriate
financial
formulae
The student
failed to correctly
identify the
issue(s);
formulae
selected were
either incorrect
or not selected
at all
Application
of formulae
The student clearly
and effectively
applies all relevant
formulae in the
most time effective
and easily
understandable
manner. Formulae
are clearly shown,
and all answers
are correct
The student
clearly and
effectively applies
all or most
relevant formulae.
Formulae are
clearly shown,
and majority of
answers are
correct
The student
applies most
relevant formulae,
but fails to obtain
all correct
answers
The student
shows a lack of
understanding in
applying
selected
formulae.
Majority of
answers are
incorrect
The student fails
to apply
formulae in the
correct manner
and all or most
of answers are
incorrect
Presentation The student
presented his\/her
solutions &
rationale in a clear,
effective and easily
understandable
manner. The end
product looks fully
professional
The student
presented his\/her
solutions &
rationale in a
clear, effective
and easily
understandable
manner with
minor flaws or
layout issues. The
end product looks
partially
professional
The student
showed a lack of
understanding
how a
professional
paper is to be
presented e.g.
with flaws in
layout;
presentation of
results; language.
However, the
paper is still
understandable
The student
showed a lack of
fully
understanding
how to
effectively and
clearly present
his\/her results.
The layout,
structure and
language is
significantly
flawed
The student fully
failed to clearly
and effectively
present his\/her
results. There is
a complete lack
of understanding
for how a
professional
paper should
look and severe
flaws in layout,
presentation of
results, structure
and language
ADDITIONAL INFORMATION<\/p>\n","protected":false},"excerpt":{"rendered":"
ACTIVITY BRIEF FOR ASSESSMENT 3ACADEMIC YEAR 2021 \u2013 2022 – SPRINGCourse BCO126 \u2013 Mathematics of Finance (3CH\/4ECTS)Instructor Florent VezinParticipation in […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[1],"tags":[],"class_list":["post-7695","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"acf":[],"yoast_head":"\n