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Question 1124449: George secured an adjustable-rate mortgage (ARM) loan to help finance the purchase of his home 5 years ago. The amount of the loan was $350,000 for a term of 30 years, with interest at the rate of 5%/year compounded monthly. Currently, the interest rate for his ARM is 3.5%/year compounded monthly, and George's monthly payments are due to be reset. What will be the new monthly payment? (Round your answer to the nearest cent.)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! adjustable rate mortgage mortgage was for $350,000 five years ago for a period of 30 years.
the rate was 3.5% per year compounded monthly.
it will now be raised to 5% per year compounded monthly.
analysis is done using the following online financial calculator.
https://arachnoid.com/finance/
the first step is to find out what the monthly payment would be for the $350,000 loan at 3.5% per year compounded monthly for 30 years.
the results of that analysis is shown below:
that analysis shows that the monthly payment are $1571.66.
the next step is to determine the remaining balance of the original loan after 5 years.
that is done by finding the present value of the mortgage at 3.5% per year compounded monthly for the remaining 25 years of the loan.
the results of that analysis are shown below:
that analysis shows that the remaining balance of the loan after 5 years is equal to $313,940.34.
that is the amount that will now be serviced at 5% per year compounded monthly for the remaining 25 years of the loan.
the next step is to determine what the monthly payments are to be for the remainder of the loan.
this is done by finding the monthly payments for a mortgage of $313,940.34 at 5% per year compounded monthly for the next 25 years.
the results of that analysis are shown below:
that analysis shows that the monthly payment will be $1835.26 for the next 25 years of the loan.
that's your solution.
i confirmed using the texas instruments BA-II business analyst calculator.
the difference between that calculator and the online calculator is that the BA-II doesn't round the answer, so it should technically be more accurate.
the BA-II showed some slight differences in the remaining balance of the loan after 5 years, but the subsequent analysis to find the monthly payment showed that the monthly payment agrees with the online calculator results when you round to 2 decimal places, so no discrepancy was noted.
we are talking very small differences.
the online calculator said the remaining balance on the loan after 5 years was $313,940.35, while the texas instruments BA=II said the remaining balance on the loan after 5 years was $313,939.7545.
that's a difference of less than a thousandth of a percent.
seeing as both calculators gave the same monthly payment of $1835.26, i'd go with that.
when using the calculators, you use the percent interest rate, not the interest rate.
the percent interest rate is equal to 100 times the interest rate.
the interest rate is the percent interest rate divided by 100.
in your problem, you were given the percent interest rate, so no modification of that part needed to be done.
you did have to convert the yearly percent interest rate to a monthly percent interest rate.
an annual percent interest rate of 3.5% per year is equal to a monthly percent interest rate of 3.5/12 = .291666666666666666.....% per month.
an annual percent interest rate of 5% per year is equal to a monthly percent interest rate of 5/12 = .4166666666666666666666....% per month.
you also needed to convert the number of years of the loan to number of months.
30 years * 12 = 360 months.
25 years * 12 = 300 months.
the inputs to online financial calculator for the different analyses are shown below:
first analysis was to find the monthly payment on the $350,000 loan for 30 years at 3.5% per year.
inputs were:
present value = 350000
future value = 0
number of monthly periods = 360
percent interest rate per month = .2916666666666666666
payment is made at the end of each monthly period
click on PMT to get -1,571.66
it is shown as negative because it is money going out.
the present value was shown as positive because it was money coming in.
second analysis was to find the remaining balance on the loan after 5 years.
all inputs were left unchanged from the first analysis except the number of monthly periods was changed from 360 to 300.
click on PV to get 313,940.34
third analysis was to find the monthly payments for a loan of $313,940.34 for the remaining 25 years of the loan.
all inputs were left unchanged from the second analysis except the percent interest rate per month was changed from .291666666666666666 to .416666666666666666.
click on PMT to get -1,835.26
once again, payment is shown as negative because it's money going out.
i also used excel to show you the monthly transactions for the critical time periods of the loan.
that is shown below:
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