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 heavy weight 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 down payment 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

3) What is the monthly fee that Mr. Andreotti will have to pay after 40 years in option B, if he finally negotiates a price reduction to 1.450.000€? He still will have to make the down payment of 1.000.000€. (15 points)

Answer 1

Total Amount of House	2450000
DownPayment	1000000
Loan Amount	1450000
Interest Rate 2.4%/12	0.002
Time Period(40*12)	480
Preset Value Factor	(1-(1+r)^-t)/r
PVF t = 480, r = 0.002	(1-(1.002)^-480)/0.002
	308.37
Monthly Payment(Loan Amount/PVF factor)	$                     4,702.14
OR
Using PMT Function of excel	$                     4,702.14
So monthly fees/payment is $4,702.14

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