14 consider the following below market financing problem for...

14. Consider the following below market financing problem for two identical properties: A B Price $130,000 $115,000 Loan Balance $80,000 (assumable) $80,000 (new loan) Down payment $50,000 $35,000 I 7% 8% Term 20 Years 20 Years a. What is the monthly payment for each loan option? b. What is the rate of return on the $15,000 investment in the first alternative? Does this seem attractive from the viewpoint of an investor?

Transcript

00:01 The martinez's are planning to refinance their home and they want to refinance and outstanding balance and create a new loan in the amount of 100 ,000 and they are given two options option one is gonna be let's see here a fixed rate mortgage with an interest rate of 5 .5 % annual compounded monthly so our n is 12 months per year and the term here is 25 years and 12 times 25 is 300 payments and then the other option so they call this a then option b is gonna be a fixed -rate mortgage at an interest rate of r is 5 .25 % and again, it's an annual rate compounded monthly but now we have let's see here.

01:26 So monthly payments monthly compounding and is still 12 now.

01:29 We have a term though of 15 years which results in 180 payments and then we want to find a monthly payment for each loan here the payment is gonna be the loan amount times r over n divided by 1 minus 1 plus r over n to the negative n t so for option a this is gonna be our 100 ,000 times 0 .055 over 12 divided by 1 minus this is an r 1 plus 0 .55 0 .055 divided by 12 to the negative 300 and it is equal to see here 100 ,000 times in parentheses 0 .055 divided by 12 and then divide by in parentheses 1 minus in parentheses 1 plus 0 .055 divided by 12 close parentheses raise it to the negative 300 closure other parentheses this is gonna be 614 and 9 cents for option a and for option b, this is gonna be the loan amount again is 100 ,000 and now we multiply that by 0 .02 0 .05 2 5 divided by n which is 12 over 1 minus 1 plus 0 .00 5 2 5 over 12 to the negative 880 so this one is gonna be so i have to let's see here insert a 2 because i have 5 to 5 instead of 5 5 5 12 1 minus 1 plus 0 .0 insert a 2 so 1 plus 0 .05 to 5 12 and then raise it to the negative 180 this time and that thing gives me a payment of 803 dollars and 88 cents for option b so these are your payment amounts and then for question b how much interest would they save if they chose to 15 -year mortgage instead of 25 -year mortgage well for option a the total paid over the life of the loan that is gonna be here we have 300 payments the payment amount is 614 with 9 cents so the total paid then it's gonna be 300 times 6 1 4 .0 9 and that is 1 8 4 2 2 7 so your total interest then is gonna be that total minus the loan amount and our loan amount was 100 ,000 so this then is gonna be 84 ,000 $227 and then for option b the total paid over the life of the loan here...

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