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

Question

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 as a loan in the beginning, and then you make monthly payments to the lender. You've decided to buy a house that is valued at $1 million. You have $350,000 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 $650,000 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, $650,000 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? $960,654.71 O $821,429.39 O $891,042.05 O $696,126.60 Which of the following statements is not true about mortgages? O The ending balance of an amortized loan contract will be zero O Mortgages are examples of amortized loans. Every payment made toward an amortized loan consists of two parts-interest and repayment of principal. If the payment is less than the interest due, the ending balance of the loan will decrease.

Explanation / Answer

Price of house $1000000 Down payment $350000 Loan Taken $650000 Yrs 30 Nominal Int Rate 9% Per Month Payment ? Monthly Interest Payment 0.09/12 0.0075 No of payments 30*12 360 Mortgage payment = P*r(1+r)^n/((1+r)^n-1) P = principal r= monthly interest rate n= number of payments (650000*0.0075(1+0.0075)^360)/((1+0.0075)^360-1) (650000*0.0075(1+0.0075)^360)/((1+0.0075)^360-1) 650000*0.0075(14.73058)/(14.73058-1) 650000*0.110479/13.73058 71811.56/13.73058 5230.045635 The monthly mortgage payment will be $5230.05 for 30 yrs mortgage loan 2) If we take 15 yr mortgage loan than monthly payment would as follows No of payments 15*12 180 (650000*0.0075(1+0.0075)^180)/((1+0.0075)^180-1) (650000*0.0075*3.838043)/(3.838043-1) 6592.732959 The monthly mortgage payment will be $6592.73 for 15 yrs mortgage loan The difference in monthly payment of 15 yrs and 30 yrs mortgage loan = 6592.732959-5230.045635 1362.687324 The difference would be $1362.68 3) Interest Payment for 30 yrs mortgage loan Total Loan Payment = 5230.045635*360 1882818 Loan Taken 650000 Interest Payment for 30 yrs mortgage loan 1232818 Interest Payment for 15 yrs mortgage loan Total Loan Payment = 6592.732959*180 1186691.4 Loan Taken 650000 Interest Payment for 15 yrs mortgage loan 536691.4 Difference in payment of interest 1232818-536691.40 696126.6 The total interest payment under 30 yrs mortgage loan will be $696126.60 more than that under 15 yrs mortgage loan 4) The following statement of mortgages is not true If the payment is less than the interest due, the ending balance of the loan will decrease

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