Question

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€ 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’ budget.

Option II: consisted in acquiring the property with a mortgage scheme for 35 years. The total price of the apartment is 875.000€. 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. Marc establishes the maximum amount they can pay monthly as 2.250€.

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)

1)In this case (yearly payments), how much has the family saved (if any) by paying yearly instead of monthly installments?

2)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.

3) 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?

Answer 1

The questions given are unclear. "In this case (yearly payments).." which is part of every question listed does not clearly mention what scenario is being referred to in the question.

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In case the family chooses the option A where the initial amount to be paid is 1650 € increasing 0.125% every month thereafter.

Total amount paid in 35 years = 1650(((1+.00125)^420) - 1)/0.00125 = 910,674.229 €

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In case the family chooses the option B to purchase the apartment.

The monthly payments to be paid by the family is:

If paying 2226.21 € monthly in a year the family will pay 2226.21*12 = 26714.52 € a year.

Thus the total amount the family would have paid in 35 years will be = 275000+ 35*26714.52 = 1210008.2 €

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If the family choose to make yearly payments instead of monthly at the same interest rate of 2.75%:

The yearly payments would have been:

The total amount paid through such yearly payments in 35 years will be = 26913.87*35 = 941985.45 €.

Thus by making yearly payments instead of monthly payments, Mr. Marco would save 268022.75 € in 35 years.

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With yearly payments of 26913.87 € the family would have paid 10*26913.87 = 260138.7 €.

To find the principle part of these payments ppmt function is used in excel.

(please ignore the $ sign in the above picture and take it as €)

Principle remaining to be paid after 10 years = 600000-118017.91 = 481982.09 €.

Thus for the principle of 481982.09 € and interest rate as 3.25%, the yearly payments will be

for the 11th year Mr. Marco will have to pay 41107.57 €.