Mathematics of Finance Task brief & rubrics
Task: Final Assignment (40% of the Final grade)
You are asked to answer all the questions in the proposed case.
This task assesses the following learning outcomes:
Assess the present value of future cash flows and the future value of regular savings, annually and periodically.
Understand the Perpetuity and annuity valuation and their factors – annual and periodical – and with various starting dates with and without
Demonstrate an ability to apply the technical skills in a practical context.
LAUNCH: WEEK 10 / DELIVERY: MAY 10Tth, 2020, 23:59HRS ON MOODLE
Submission file format: Word document with all the answers, clearly identifying all steps, results, and including comments besides each answer.
Task (100 points)
The Andreotti family—comprising Mr. Andreotti, aged 40, Mrs. Andreotti, aged 38, and their three young children— relocated to
Barcelona in 2020 when Mr. Andreotti received a job offer from a leading investment banking giant. For the next six years, they
rented a three-bedroom condominium for 2.000€ in Barcelona per month, which included parking and condominium fees.
While renting made life easy, the Andreotti family began weighing the pros and cons of purchasing a flat, in the same building,
that became available in June 2020. In the past three years, the real estate market had softened somewhat, and the cost of the
flats were stable. The idea of home ownership as a form of pension investment appealed to the couple. The monthly rents could
be used for mortgage payments instead.
While searching for the right property they found a nice apartment with 200 square meters, very close to Diagonal-Numancia,
one of the best locations of the city.
The apartment was owned and been promoted by a state-owned construction company and was offering to type of alternatives:
Option A: renting the apartment with a perpetual contract, meaning for ever and ever. The Andreotti family thought that could be
a good solution for them.
The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1.600€ per
month. The contract contained a clause stating that the rent price will be growing at a 0.1% monthly.
At the same time, they were not forced to ask for a loan, which represented a heavy weight in Mr. Andreotti´s shoulders.
Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was demanding an initial
down payment of 1.000.000€. The total price of the apartment was still not clear, it seems there was some space for negotiation.
Mr. Andreotti new that the interest applicable rates were very attractive, around 2.4% compounded monthly, this is supposed to
be the market rate for this type of activities.
Mr. Andreotti is fixing the maximum amount he can pay monthly in 2.000€.
1) What is the maximum amount that Mr. Andreotti should pay? Show the calculations and explain why. (15 points)
2) What is the total amount that Mr. Andreotti will pay in total after 40 years? (15 points)
3) What is the present value of the rental contract offered by the owner as option A? (15 points)
4) Mr. Andreotti believes that he might be interested in selling the apartment in 40 years’ time, this is when he is planning to
If the interest rates remain at the existing level, what will be the price of the apartment in that moment? (15 points)
5) Mr. Andreotti is very happy for knowing how to calculate future values and present values, because this helps him in
taking this type of decisions. Having said that he wonders what the future value of the rental contract could be. Can you
help him? Explain your answer and show your calculations. (10 points)
6) We are still thinking that the price of the apartment is very expensive, we believe we could convince the bank of making
payments only once a year, at the end of the year. The interest rate would still be the same 2.4%, how much money have
we saved with this action?
a) In the payments for each year? b) in the total amount paid for the whole period? c) what is the present value of the
7)There is a risk according to Mr. Andreotti that the interests may rise after the first 5 years. If this is the case, and the new
interest rate is 5%, just after the first 5 years, how much will then be the monthly payments for the remaining 35 years of
mortgage? (Hint the total initial value of the loan is depends of the offered purchase price in point 2). Explain your answer and
show your calculations. (15 points)
The student demonstrates understands the concepts and uses the
right approach with the right formulas
The student explains the calculations, and which is the theory behind
The student applies the right numbers in the formulas
The student finds the right answer
The student shows an accurate presentation
Points are at the end of each question.
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