please answer question c, because a and b have been answered 6. THE BUILDING OF
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please answer question c, because a and b have been answered
6. THE BUILDING OF NEW HOUSES Suppose a family is trying to decide whether to build a new house. They find a lot that costs $120,000 and learn that building the house will cost $180,000. They have $40,000 saved to make a down payment. a. Ignoring various other costs (legal fees, taxes, and the like), what is the size of mortgage required for this fam- ly to purchase this house? b. Use a search engine to find a mortgage calculator and retrieve the monthly payment for this mortgage when the mortgage interest rate is 4% and the period of amor- tization (the length of time to repay the entire mortgage) is 25 years. Use a search engine to find a mortgage calculator and retrieve the monthly payment for this mortgage when the mortgage interest rate is 6% and the period of amortization (the length of time to repay the entire mortgage) is 25 years Explain the effect of interest rates on the decision to purchase the house.Explanation / Answer
Answer [Sub-Question ©]
Total cost of the completed house : $ 120,000 + $ 180,000 : $ 300,000
Less: Down payment (Paid by the family directly) : $ 40,000
Amount of mortgage required : $ 260,000
Case (a): If the mortgage is availed at 4% p.a, the Equated Monthly Instalments for 25 years would be $ 1372.
At the end of Year 5, the outstanding amount of loan would be $ 226,472/-.
Situation (1) Optimistic
If the price of the house increases by 3% for the next 5 years, the price of the house at the end of Year 5 would be -
$ 300,000 x 1.03 x 1.03 x 1.03 x 1.03 x 1.03 = $ 347,782.22
Upon sale of the house after 5 years, the family will realise $ 347,782.22. They will have to pay the outstanding mortgage liability $ 226,472/- using this amount.
Hence, balance amount available in hand after repaying outstanding mortgage
= $(347,782.22 - 226,472) = $ 121,310.22
Hence, if the interest rate for the mortgage is 4% p.a and the optimistic condition prevails, the family will have $ 121,310.22 in their hand after Year 5.
Situation (2) Pessimistic
If the price of the house decreases by 1% for the next 5 years, the price of the house at the end of Year 5 would be -
$ 300,000 x 0.99 x 0.99 x 0.99 x 0.99 x 0.99 = $ 285,297.01
Balance amount available with the family, after repaying the outstanding mortgage
$ (285,297.01 - 226,472) = $ 58,825.01
Hence, if the interest rate for the mortgage is 4% p.a and the pessimistic condition prevails, the family will have $ 58,825.01 in their hand after Year 5.
Case (b): If the mortgage is availed at 6% p.a, the Equated Monthly Instalments for 25 years would be $ 1675.
At the end of Year 5, the outstanding amount of loan would be $ 233,823/-.
Situation (1) Optimistic
If the price of the house increases by 3% for the next 5 years, the price of the house at the end of Year 5 would be -
$ 300,000 x 1.03 x 1.03 x 1.03 x 1.03 x 1.03 = $ 347,782.22
Upon sale of the house after 5 years, the family will realise $ 347,782.22. They will have to pay the outstanding mortgage liability $ 233,823/- using this amount.
Hence, balance amount available in hand after repaying outstanding mortgage
= $(347,782.22 - 233,823) = $ 113,959.22/-
Hence, if the interest rate for the mortgage is 6% p.a and the optimistic condition prevails, the family will have $ 113,959.22 in their hand after Year 5.
Situation (2) Pessimistic
If the price of the house decreases by 1% for the next 5 years, the price of the house at the end of Year 5 would be -
$ 300,000 x 0.99 x 0.99 x 0.99 x 0.99 x 0.99 = $ 285,297.01
Balance amount available with the family, after repaying the outstanding mortgage
$ (285,297.01 - 233,823) = $ 51474.01
Hence, if the interest rate for the mortgage is 6% p.a and the pessimistic condition prevails, the family will have $ 51,474.01 in their hand after Year 5.
Thus, in all the four situations explained above, the family will have sufficient surplus cash at the end of Year 5, after repaying the mortgage liability.
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