Question 1118310: Find the monthly payment and estimate the remaining balance. Assume interest is on the unpaid balance.
Twenty-year mortgage for $290,000 at 3.54 %; remaining balance after 12 years.
The monthly payment is$?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the interest rate is 3.54% per year.
divide that by 12 to get an interest rate of (3.54/12)% per month.
the present value of the loan is 290,000.
the duration of the loan is 12 years * 12 = 144 months.
the standard assumption is that the payments are made at the end of each month.
you could use a time value of money / financial calculator, to find the monthly payments.
the calculator i'm using can be found at https://arachnoid.com/finance/
using this calculator, you would make the following inputs.
present value = 290,000
interest rate per month = (3.54/12) = .295%
number of months = 20*12 = 240
payments are made at the end of each month.
future value = 0
payments per month = 0 or blank (this is what you want to find).
this is what your inputs look like.
you then click on PMT.
your results would look like this.
the calculator tells you that your payments are 1,687.85 per month.
the value is shown as negative because this is money going out.
the present value is shown as positive because this is money coming in.
to find the remaining balance after 12 years, you would do the following, using this calculator.
present value = 0.
future value = 0.
payments per month = -1687.85 per month.
interest rate = .295% per month.
payments are made at the end of each month.
number of months = 20 - 12 = 8 * 12 = 96.
that's the number of months remaining on the loan after 12 years.
your inputs would look like this.
you would then click on PV.
your result would look like this.
the calculator tells you that the present value of the loan is equal to 140,930.76.
the present value of that loan is the remaining balance on the original loan after 12 years.
i also did this using the TI-BA-II calculator to confirm the answer is correct.
the TI-BA-II confirmed it is correct.
i used the remaining balance feature of the TI to do this.
i also did this using excel to also confirm the answer is correct.
in both the TI and Excel, a different way of calculating the result was used, with the result being the same.
this indicates the result is most probably good.
you can see the result from excel.
it is the remaining balance after 12 * 12 = 144 months.
the first printout shows the beginning of the 20 year loan.
the second printout shows the remaining balance after 144 months.
the third printout shows the remaining balance at the end of the 20 year loan.
it is 0 as it should be.
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