Question
In: Finance
The Marconi family—comprising Mrs. Marconi, aged 40, Mr. Marconi, aged 38, and their three young children—...
The Marconi family—comprising Mrs. Marconi, aged 40, Mr. Marconi, aged 38, and their three young children— relocated to Barcelona in January 2020 when Mrs. Marconi received a job offer from a leading investment banking giant. They rented a three-bedroom condominium in Barcelona for 2.000€ per month, which included parking and condominium fees. While renting made life easy, the Marconi family began weighing the pros and cons of purchasing a flat, in the same building, that became available in June 2020. In the past three years, the real estate market had softened somewhat, and the cost of the flats were stable. The idea of home ownership as a form of pension investment appealed to the couple. The monthly rents could be used for mortgage payments instead. While searching for the right property they found a nice apartment with 200 square meters, very close to Diagonal-Numancia, 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 A: renting the apartment with a perpetual contract, meaning forever. The Marconi family thought that could be a good solution for them. The family was very happy living in that area, and they had the chance to live there forever at an offered price of 1,600 EUR the first month, and the rent price will be growing by a 0.1% monthly. At the same time, they were not forced to ask for a loan, which represented a heavy burden off the Marconi’s. Option B: consisted in acquiring the property with a mortgage scheme for 40 years. The total price of the apartment is 800.000€. The family can pay an initial down payment of 200,000 EUR and the rest (600,000 EUR) to be paid in constant monthly payments with an annual interest rate of a 2.4% compounded monthly. Mrs. Marconi establishes the maximum amount they can pay monthly as 2.000€
1)In case of taking option A, what is the amount of the monthly payment the Marconi family should pay in 40 years (in month 480)? (only the amount to be paid that month) Show the calculations and explain why.
2)In case of taking option A, how much money will have the Marconi family paid in total after 40 years?
3)If the Marconi family decides to leave Barcelona in 10 years, back to Italy, what is the present value of the rental contract offered by the owner as option A? (take the 2.4% compounded monthly as the interest/discount rate)
4) If Mrs. Marconi decides to buy the apartment, and accepts Option B, what will be the amount of each monthly payment to be done during the next 40 years?
5)Mrs. Marconi believes that, if she takes option B and acquires the ownership of the flat, she might be interested in selling the apartment in 40 years’ time, that is to say, when she has already paid it all. If she wants to recover absolutely all the money invested (initial payments plus all monthly payments done), what will be the price she will ask for that apartment at that moment? (don’t use the concept of Time Value of Money here, it is just about finding how much has Mrs. Marconi paid in total)
6)Mrs. Marconi is very happy for knowing how to calculate future values and present values, because this helps her in taking this type of decisions. Having said that, she wonders what the future value of the flat will be in 40 years, if the interest rate for this type of operations is an annual 1.5% (comp. monthly). Find the Future Value of that apartment in 40 years. Explain your answer and show your calculations.
7)The family is still thinking that the monthly payments they’ll have to afford during the next forty years (we are still in option B) are too much, and they believe they could convince the seller of making constant payments only once per year, at the end of each year. The interest rate would still be the same 2.4% (but now that would be compounded yearly instead of monthly). What is the amount of the yearly payment to be done?
8)In this case (yearly payments) what is the total amount they’ll have paid in total after 40 years? (again, just find how much has Mrs. Marconi paid in total)
9)In this case (yearly payments), how much has the family saved (if any) by paying it yearly instead of monthly?
10)In case that the Marconi family pays the pending amount in yearly payments, the owner can only grant them a 2.4% during the first 10 years. There is the possibility that, after the first 10 years the interest rate increases to a 3.0% for the remaining 30 years. How much should the Marconi family pay per year from year 11 onwards if this occurs?
11-answer only 5-10 pls
Solutions
Expert Solution
| Answer to Question 1: | |||||||||||||
| The question requires what would be the payment to be made after 40 years for the 480th month | |||||||||||||
| According to Option A, First rental Payment to be paid is EUR 1600 | |||||||||||||
| There after the rental payment to be paid would be growing 0.1% monthly | |||||||||||||
| Accordingly I am providing the formula using below table for calculation of monthly Rent | |||||||||||||
| First month Payment = | EUR 1600*(1) | 1600 | |||||||||||
| Second month Payment = | EUR 1600*(1+0.1%) | 1601.6 | |||||||||||
| Third month Payment = | EUR 1600*[(1+0.1%)]^2 | 1603.202 | |||||||||||
| Fourth month Payment = | EUR 1600*[(1+0.1%)]^3 | 1604.805 | |||||||||||
| Nth month Payment = | EUR 1600*[(1+0.1%)]^(N-1) | ||||||||||||
| 480th month Payment = | EUR 1600*[(1+0.1%)]^(480-1) | 2582.516 | |||||||||||
| Answer to Question 2: | |||||||||||||
| The question requires sum of total monthly rental payments made in the first 40 years(i.e., 480 months payments) under Option A | |||||||||||||
| The monthly payments are in a Geometric Progression Growing at the common ratio(r) of (1+0.1%) i.e., r=1.001 | |||||||||||||
| First No. in the series of Geometric Progression (a) is 1600 | |||||||||||||
| Sum of first n terms in a geometric progression is = a*([1-(r^n)]/[1-r]) | |||||||||||||
| Sum of first 480 monthly payments in a geometric progression is = 1600*([1-(1.001^480)]/[1-1.001]) | |||||||||||||
| Which equals to | 985099 | ||||||||||||
| Answer to Question 3: | |||||||||||||
| The Question requires to calculate present value of rental contract of 10 years under Option A | |||||||||||||
| Given discount rate to be taken is 2.4% componded monthly | |||||||||||||
| I would show show the discounting of first four payments look firstly | |||||||||||||
| First month Payment = | [EUR 1600*(1)] | ||||||||||||
| Second month Payment = | [EUR 1600*(1+0.1%)]/(1+0.024) | ||||||||||||
| Third month Payment = | [EUR 1600*[(1+0.1%)]^2]/(1+0.024)^2 | ||||||||||||
| Fourth month Payment = | [EUR 1600*[(1+0.1%)]^3]/(1+0.024)^3 | ||||||||||||
| Nth month Payment = | [EUR 1600*[(1+0.1%)]^(N-1)]/(1+0.024)^(N-1) | ||||||||||||
| The Discounting of each months payment is in a Geometric progression Growing at the common ratio (r) of (1+0.1%)/(1+0.024) i.e., r=0.9775 | |||||||||||||
| First No. in the series of Geometric Progression (a) is 1600 | |||||||||||||
| as already provided in Answer 2 Sum of first n terms in a geometric progression is = a*([1-(r^n)]/[1-r]) | |||||||||||||
| Therefore sum of Discounted 10 years (i.e., 120 monthly payments) in the geometric progression is = 1600*([1-(0.9775^120)]/[1-0.9775]) | |||||||||||||
| Which equals to | 66477.18 | ||||||||||||
| Answer to Question 4: | |||||||||||||
| The question requires If Option B is accepted what would be the monthly payments to be made | |||||||||||||
| Given Total Cost of the Apartment = EUR 800,000 | |||||||||||||
| Initial downpayment that the family are willing to make is = EUR 200,000 | |||||||||||||
| Remaining Amount of EUR 600,000 is to be paid in 40 years (i.e., monthly) in equal installments | |||||||||||||
| Equated Installment formula is | {P*[i*((1+i)^n)]}/((1+i)^n)-1 | ||||||||||||
| Where P equals to Principal amount to be collected | |||||||||||||
| And I is the discount rate , n is no. of installments | |||||||||||||
| in our Question P= EUR 600,000; i = 2.4%; n= 480 | |||||||||||||
| Therefore Equated Annual installment is | (600000*(0.024*((1+0.024)^480)))/((1+0.024)^480)-1 | ||||||||||||
| Which equals to | 14400.16 | ||||||||||||
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Answer to Question 5:
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jeff jeffy answered 1 year ago