Question

The Marco family — comprising Mrs. Marco aged 40, Mr. Marco, aged 3 9 , and their three young children — relocated to Barcelona in January 2020 when Mrs. Marco received a job offer from a n international firm . They rented a three - bedroom condominium in Barcelona for 2. 1 00€ per month, which included parking and fees.

While renting made life easy, the Marc o 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 f or 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 perpet ual 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 , 6 5 0 EUR the first month, and the rent price will be growing by a 0.1 25 % monthly. This option would prevent the Marco family from applying for a loan, which represented a heavy burden off the family’ budget .

Option II : consisted in acquiring the property with a mo rtgage scheme for 35 years. The total price of the apartment is 8 75 .000€. The family can pay an initial down payment of 2 75 , 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 monthl y.

Mrs. Marc establishes the maximum amount they can pay monthly as 2. 25 0€.

- In case of taking option I , what is the amount of the monthly payment the Marco family should pay in 35 years (in month 4 2 0) ?

( only the amount to be paid that month , s how the calcu lations )

- 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 o ffered 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’ time. If she wants to recover a ll the money invested (initial payments plus all monthly payments done), what will be the p rice 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 d ecisions. S he wonders what the future value of the flat will be in 35 years, if the interest rate for this type of operations is an a nnual 1. 7 5% (comp. monthly). Find the Future Value of that apartment in 35 years.

- The Marco family thinks that the monthly payments they’ll have to afford during the nex t thirty five years are too much, and believe s the seller could be convinced about maki ng 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?

I need Questions1-2-3

Answer 1

Question 1:

First month installement = 1650 Eur

Interest = 0.125% monthly

Time 35 years i.e 420 in months

The future value is given by

FV = PV * (1+r)^n

1650* (1+0.125%)^420

= 2788.34

Question 2:

P = 1650

r = 0.125%

n =420

= 1650*((1+.125%)-1)/0.125% = 910,674.23

Question 3:

P = 1650

r= 2.75%

n = 12*10 =120

Substituting the formula we get PV as 57,686.17