Extract
[...] This sum can be written in a simplified formula: Total amount = U0 * (1-q**number of terms) / with U0 the first term of the sequence, q the reason, and the number of term being equal to 30, because we start from n=0. In applying this calculation, we obtain: Total amount spent after 30 years = 856,357 euros. Thus, over 30 years, the rental property returns to 856 357 ?. Now, we will focus on the second option: the purchase. As mentioned in the introduction, the property is at the initial price of 285,000 euros. [...]
[...] Real Estate: Should We Rent or Buy? - Grand Oral of Mathematics Grand Oral Mathematics - Real Estate As a future university student, I will be moving to a big city alone in a few months. From the moment I was accepted on Parcoursup, I discovered through numerous websites and agencies how difficult it is to find a housing, not only because of scams and low availability, but also and above all because of the prices, which continue to rise. [...]
[...] We assume that the landlord will implement an annual increase of 3%. We can therefore consider the rent as a geometric sequence defined by recurrence, i.e., a sequence having a first term U0 = 18,000, associating with each year n the amount paid by the family in euros. Thus, for this first term, at year n = the family will have paid 18,000 euros. A geometric sequence is used here because each year, the amount paid by the couple increases by i.e., a fixed percentage of the amount of the previous year, which perfectly corresponds to the definition of a geometric sequence where each term is obtained by multiplying the previous term by a constant factor. [...]
[...] The initial debt is 226,350 euros. The first year, the value of the interest is therefore 226,350*0.035 = 7,922.25 euros. Which means that the first year, the capital paid for the amortization of the house is equal to the annuity - the interest, so we have: 13,734 - 7,922.25 = 5,811.75 euros. The first year, the debt to be paid is very large so the interest to be paid are also. The second year, the debt to be paid has decreased: it is equal to the initial debt - the amortization paid the previous year. [...]
[...] In our case, the profitability threshold is reached from the 18th year, that is, in 2043. However, this model presents several limitations. It does not take into account the possible resale of the property, the possible increase in its value, nor the maintenance or repair costs. Similarly, the evolution of interest rates or the professional stability of the couple are not considered. In reality, the choice between buying or renting also depends on many personal, financial, and sometimes psychological factors. This analysis has nonetheless allowed us to bring a rigorous mathematical light to our problem. [...]
