You\'ve decided to buy a house that is valued at $1 million. You have $500,000 t
ID: 2812079 • Letter: Y
Question
You've decided to buy a house that is valued at $1 million. You have $500,000 to use as a down payment on the house, and want to take out a mortgage for the remainder of the purchase price. Your bank has approved your $500,000 mortgage, and is offering a standard 30-year mortgage at a 9% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your mortgage payment will be month. (Note: Round the final value of any interest rate used to four decimal places.) per Your friends suggest that you take a 15-year mortgage, because a 30-year mortgage is too long and you will pay a lot of money on interest. If your bank approves a 15-year, $500,000 loan at a fixed nominal interest rate of 9% (APR), then the difference in the monthly payment of the 15-year mortgage and 30-year mortgage will be ?(Note: Round the final value of any interest rate used to four decimal places.) It is likely that you won't like the prospect of paying more money each month, but if you do take out a 15-year mortgage, you will make far fewer payments and will pay a lot less in interest. How much more total interest will you pay over the life of the loan if you take out a 30-year mortgage instead of a 15-year mortgage? O $631,866.64 O $685,414.66 O $738,962.68 $535,480.20 Which of the following statements is not true about mortgages O The ending balance of an amortized loan contract will be zero. Mortgages always have a fixed nominal interest rate O Mortgages are examples of amortized loans. O The payment allocated toward principal in an amortized loan is the residual balance-that is, the difference between total payment and the interest due.Explanation / Answer
House Price = $ 1000000 and Downpayment = $ 500000
Total Mortgage Taken (Borrowing) = 1000000 - 500000 = $ 500000
APR = 9 % per annum or 0.75 % per month (9/12 = 0.75)
Mortgage Tenure = 30 years or 360 months
The monthly mortgage payment would be such that the total present value of these 360 monthly mortgage repayments is equal to the current value of the mortgage borrowing. Such a borrowing which pays off both the accruing interest and the principal borrowing through periodic equal repayments is known as a fully amortized loan.
Let the monthly equal mortgage repayments be $ K
Therefore, 500000 = K x (1/0.0075) x [1-{1/(1.0075)^(360)}]
K = $ 4023.1131 approximately.
If the mortgage is taken for a duration of 15 years of 180 months, only the repayment tenure changes with everything else remaining constant. Let the monthly repayment in the 15-year mortgage be $ M
500000 = M x (1/0.0075) x [1-{1/(1.0075)^(180)}]
M = $ 5071.3329
The difference in monthly repayments = 5071.3329 - 4023.1131 = $ 1048.2198
Total Interest Paid in the 30 Year Mortgage = Monthly Repayments x 360 - Initial Borrowing = (4023.1131 x 360) - 500000 = $ 948320.716
Total Interest Paid in the 15 Year Mortgage = Monthly Repayments x 180 - Initial Borrowing = (5071.3329 x 180) - 500000 = $ 412839.922
Extra Interest Paid in the 30 Year mortgage as compared to the 15 Year mortgage = 948320.716 - 412839.922 = $ 535480.794 ~ $ 535480.2
Hence, the correct option is (d).
Among all the statements listed the first one is true as mortgages are usually fully amortizable loans with final loan account value equal to zero. Hence, the ending value of the amortized loan contract will be zero. Further, mortgages are definitely examples of amortized loan contracts as already mentioned and proven. The payments assigned to principal in an amortized loan is indeed equal to the difference between the periodic mortgage repayments and the interest due on the mortgage, as interests accrued have a higher priority of repayment over outstanding mortgage principal. The second statement, however, is NOT TRUE as mortgages do not always have fixed nominal interest rates. Mortgages can have variable interest rates as well which are popularly known as adjustable rate mortgages.
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