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.

Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The ownership was demanding an initial down payment of 1.000.000€. The total price of the apartment was still not clear, it seems there was some space for negotiation.

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.

Mr. Andreotti is fixing the maximum amount he can pay monthly in 2.000€.

1. What is the maximum amount that Mr. Andreotti should pay? Show the calculations and explain why. (15 points)

2. What is the total amount that Mr. Andreotti will pay in total after 40 years? (15 points)

3. What is the present value of the rental contract offered by the owner as option A? (15 points)

3. Mr. Andreotti believes that he might be interested in selling the apartment in 40 years’ time, this is when he is planning to retire.

If the interest rates remain at the existing level, what will be the price of the apartment in that moment? (15 points)

5. Mr. Andreotti is very happy for knowing how to calculate future values and present values, because this helps him in taking this type of decisions. Having said that he wonders what the future value of the rental contract could be. Can you help him? Explain your answer and show your calculations. (10 points)

6)  We are still thinking that the price of the apartment is very expensive, we believe we could convince the bank of making payments only once a year, at the end of the year. The interest rate would still be the same 2.4%, how much money have we saved with this action?

a) In the payments for each year? b) in the total amount paid for the whole period? c) what is the present value of the savings?

Answer 1

The initial downpayment demanded is 1,000,000 Euro. If the mortgage amount is assumed to be the same, then the maximum monthly amount that Mr. Andreotti should pay as Installment will be,

EMI=P*r*[(1+r)^n/((1+r)^n)-1] where, P=principal amount=1000000, r=rate of interest=2.4% or, 0.002/month & n=no. of periods=40*12 or 480

Therefore, EMI=1000000*0.002*[(1.002^480)/((1.002^480)-1)] or, 3242.8584 Euro.

Total amount that Mr. Andreotti will pay in total is EMI*no. of periods 3242.8584*480 or, 1556572.032 Euro

If Mr. Anreotti decides to fix the monthly pay at 2000 Euro then maximum amount he can avail as mortgage will be, EMI*(1-(1+r)^-n)/r where, EMI=2000 and r=0.002 i.e. 2000*(1-((1.002)^-480))/0.002 or, 616739.85 Euro

Total amount payable if EMI is fixed at 2000 Euro will be = 2000*480 or, 960000 Euro.

The present value of the rental contract offered by the owner as option A i.e. to pay an amount of 2000 Euro per month for six years will be = Monthly rent*(1-(1+r)^-n)/r i.e. 2000*(1-((1.002)^-72))/0.002 or, 133987.72 Euro (Here n=12*6 or, 72)

Edit: You have to calculate the Future Value of the monthly payments made for which we will use the formula = Monthly payments*((1+r)^n-1)/r
Ans to (Q.4): The price of the apartment he will expect after 40 years=3242.8584*((1.002^480)-1)/0.002 or, 2609193.79 (This is because had he saved the EMI paid and invested in bank he would have garnered the above amount).

Applying the same formula we can get the answer to Q.5: Future value of the rental contract=2000*((1.002^480)-1)/0.002 or, 1609193.78