Question 1206142: The Taylors have purchased a $320,000 house. They made an initial down payment of $10,000 and secured a mortgage with interest charged at the rate of 6%/year on the unpaid balance. Interest computations are made at the end of each month. If the loan is to be amortized over 30 years, what monthly payment will the Taylors be required to make? (Round your answer to the nearest cent.)
$
What is their equity (disregarding appreciation) after 5 years? After 10 years? After 20 years? (Round your answers to the nearest cent.)
5 years $
10 years $
20 years $
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! initial down payment was 10,000.
amount left to be mortgaged was 310,000.
interest rate was 6% per year, compounded monthly = .5% per month.
payments were assumed to be made at the end of each month.
amount required to be paid at the end of each month is 1858.61, according to financial calculator at https://arachnoid.com/finance/
inputs to the calculator were:
present value = -310,000
future value = 0
number of time periods = 30 years * 12 months per year = 360
interest rate per month = 6% / 12 = .5%
payments are made at the end of each month.
output is the payment required at the end of each month.
this is what the results look like.
5 years * 12 = 60 months.
10 years * 12 = 120 months.
20 years * 12 = 240 months.
original number of time periods of the mortgage is 30 years * 12 = 360.
360 - 60 = 300 months remaining after 5 years.
360 - 120 = 240 months remaining after 10 years.
360 - 240 = 120 months remaining after 20 years.
payment of 1858.61 at the end of each month gets you a present value of:
288469.02 after 300 months (what you still owe after 5 years).
259426.22 after 240 months (what you still owe after 10 years).
167411.42 after 120 months (what you still owe after 20 years).
here are what those results look like.
remaining balance after 60 months (5 years).
remaining balance after 120 months (10 years).
remaining balance after 240 months (20 years).
the original present value of the loan = 310,000
310,000 - 288,469.02 = 21,540.97
310,000 - 259,426.22 = 50,573.78
310,000 - 167,411.42 = 142,588.58
what this is telling you is that:
you earned 310,000 minus 288,469.03 = 21,540.97 of equity after 60 months (remaining period on the loan was 300 months).
you earned 310,000 minus 259,426.22 = 50,573.78 of equity after 120 months (remaining period on the loan was 240 months).
you earned 310,000 - 167,411.42 = 142,588.58 of equity after 240 months (remaining period on the loan was 120 months).
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