Question 1206142
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 <a href = "https://arachnoid.com/finance/" target = "_blank">https://arachnoid.com/finance/</a>

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.


<img src = "http://theo.x10hosting.com/2024/021901.jpg">


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).


<img src = "http://theo.x10hosting.com/2024/021902.jpg">


remaining balance after 120 months (10 years).


<img src = "http://theo.x10hosting.com/2024/021903.jpg">


remaining balance after 240 months (20 years).


<img src = "http://theo.x10hosting.com/2024/021904.jpg">


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).