Question 1104548: Raymond took out a 25-year loan from his bank for $135,000 at an APR of 3.6%, compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80% of the balance, what prepayment fee would Raymond be charged for paying off his loan 5 years early?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! not exactly sure if it's done exactly this way, but this is what i think.
25 year loan at 3.6% interest yields.
number of month = 25 * 12 = 300 months.
annual percent interest of 3.6% / 12 = monthly percent interest of .3.
the number of monthly payments on a loan of 135,000 for 300 months at .3% per month = 683.1036618.
if you pay 683.1036618 every month for 300 months, the remaining balance on the loan is 0.
if you pay 683.1036618 every month for 240 months, the remaining balance on the loan is 37,457.91765.
so, if the loan is payed off 5 years early, there would still have been 37,457.9176 remaining balance on the loan.
the penalty would be assessed to this amount.
assuming that they would simply take 1/2 of 3.6% = 1.8%, then the penalty assessed would be .018 * 37,457.9176 = 674.2425176.
if you assume they are using monthly interest rate for 6 months, then the penalty assessed would be 37,457.9176 * (1 + .036/12) ^ 6 = 38137.23726 - 37457.9176 = 679.3196094.
it's a very small difference that really depends on which way they are calculating 6 months worth of interest.
the key component here is what would have the remaining balance have been after 240 months of paying the loan off at 683.1036618 dollars a month.
that remaining balance would have been 37,457.9176 dollars.
the following excel spreadsheet printout shows this to be true.
first printout shows you remaining balance of the loan in the beginning.
second printout shows you remaining balance of the loan at the end of month 240.
third printout shows you remaining balance of the loan at the end of month 300.
the actual penalty charged depends on how they calculate a half a year's worth of interest.
that penalty will be assessed on what the remaining balance of the loan would have been had they not paid the loan off early.
at least that's my opinion.
this opinion is based on my logical assessment of the problem.
i have no idea how it's actually done, since i don't work for the bank in question.
to get better information on the penalty and how it's assessed, you would have to speak to a representative of the bank.
i am reasonably confident, however, that the remaining balance of the loan at the end of month 240 is the amount indicated.
since the loan was originally scheduled to go 300 months, then paying off the loan by the end of month 240 would be 5 years early, because 5 years is equal to 60 months and 300 - 60 is equal to 240.
|
|
|
