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Question 1206579: Fifteen years ago a couple purchased a house for $150,000.00 by paying a 20 % down payment and financing the remaining balance with a 30-year mortgage at 6.84% compounded monthly.
(a) Find the monthly payment for this loan.
Monthly Payment:
[Note: Your answer is a dollar amount and should have a dollar sign and exactly two decimal places.]
(b) Find the balance of the loan after 16 years and after 17 years?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the house cost 150,000.
they paid 20% down = 30,000 down.
the mortgage was for 150,000 - 30,000 = 120,000.
the mortgage was for 30 years at 6.84% per year.
multiply the years by 12 to get 360 months.
divide the annual interest rate by 12 to get .57% per month.
using the financial calculator at https://arachnoid.com/finance/, i get a payment of 785.51 due at the end of each month for the duration of the loan.
here's what the results from using that calculator look like.
the end of the 16th year of the loan is the end of month 192 of the loan and the end of the 17th year of the loan is the end of month 204 of the loan.
the remaining months of the loan are 360 - 192 = 168 after 16 years and 360 - 204 = 156 after 17 years.
you can use the same calculator to see what the present value of those loans are at the specified number of months left at the same interest rate per month.
here's what that analysis looks like.
the first analysis shows that the present value of the loan for 168 months, at the same payments per month and the same interest rate per month of the original loan, is equal to 84,771.98 dollars.
that's the remining balance of the original loan after 16 years.
the second analysis shows that the present value of the loan for 156 months, at the same payments per month and the same interest rate per month of the original loan, is equal to 81,028.35 dollars.
that's the remaining balance of the original loan after 17 years.
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