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€.

• The Marco family thinks that the monthly payments they’ll have to afford during the next thirty five years are too much, and believes the seller could be convinced about making 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?

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

Answer 1

1) What is the amount of the yearly payment to be done?

The first year payment to be done is 2250*12=27000

From next year the payment will be, 2250*(1+r)^n, where n is the nth year

2) what is the total amount the Marco family will have paid in total after 35 years?

Total amount with compound interest will be C*(1+r)^n

This will be 27000*12(1+0.0275)^35=837353.97

3) how much has the family saved (if any) by paying yearly instead of monthly installments?

Difference between 2250*12*35(1.0275)^12=1308620.67 and 837353.97, which gives 471266.7

The family was able to save 471266.7