Question

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 heavyweight in Mr. Andreotti ́s shoulders.

Option B:
Consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was also demanding an initial downpayment of 1.000.000 in this case. 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.

1)Mr. Andreotti believes that he might be interested in selling the apartment in 40 years’ time (option B), this is when he is planning to retire. With that amount sold, he may be able to retire. So he will be receiving from the Bank a monthly payment for his retirement. How much will he earn if he lives 25 years?

2)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 and to know the savings of each option. What is the equivalent value of the perpetual contract in year 40 to allow him to compare with option B? Explain your answer and opinion according to the data and calculations done. What are the pros and cons of renting or buying a house then?

Answer 1

Option 1
Monthly Rent	1600
Monthly increase	0.10%
Total No of Months	480
Total Amount of rent paid in 40 years	768,504
T*P+(1+R)^T
Where T = total number of months, P = Rent, R = monthly increase %
IF Apartment is bought by initial downpayment through mortgage
Down payment	1000000
Intere rate	2.40%
No of months	480
Monthly Payment	3,243
Total payment over 40 years	1,556,640

Based on the above workings it can be concluded that the option to rent is cheaper as compared to mortgage.

Further information on the total value of the property is required so as to compute what will Mr Andreotti will earn after 25 years from Bank.