AaAa Mortgages, loans taken to purchase a property, involve regular payments at

Question

AaAa Mortgages, loans taken to purchase a property, involve regular payments at fixed intervals and are treated as reverse annuities. Mortgages are the reverse of annuities, because you get a lump-sum amount and then you make monthly payments to the lender. as a loan in the beginning, You've decided to buy a house that is valued at 'si million. You have $300,000 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 $700,000 mortgage, and is offering a standard 30-year mortgage at a 10% fixed nominal interest rate (called the loan's annual percentage rate or APR). Under this loan proposal, your month. (Note: Round the final value of any interest rate used to four decimal places.) mortgage payment will be 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, $700,000 loan at a fixed nominal interest rate of 10% (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 ife of the loan if you take out a 30-year mortgege instead of a 15-year mortgage? O $1,092.515.0o $1,183,258.37 O $1,011/771.65 O $857/433.60 O Type here to search

Explanation / Answer

Monthly payment M = P* [ r(1+r)n ] /[ (1+r)n-1]
where P is the principal amount, here it is $1000000 - 300000 = 700000
M is the monthly payment
r is the monthly rate calculated as r/12 = 10/12 = 0.8333% or 0.0083
n = number of months of payment

M = 700000* [ 0.0083(1+0.0083)360 ]/ [(1+0.0083)360-1
    = 700000*[ 0.1653/ 18.8374
   = $6143.0010 Answer

b Similarly, for 15 year
M = 700000* [ 0.0083(1+0.0083)180 ]/ [(1+0.0083)180-1
= 700000* [ 0.0371 / 3.4539 ]
   = $7522.2358
Difference in the monthly payment = 7522.2358 - 6143.0010
   = $1379.2348 Answer

c On a 30-year mortgage Total payment to be made = (6143.0010*360) = 2211480.3600
On a 15 year mortagage total payment to be made = (7522.2358 *180) = 1354002.4440
Therefore, excess interest paid = $857477.916

option d> $857433.60 Answer
Note: ( rounding off has resulted in the difference). i have rounded off the final results to four decimal places hence the above result.

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