Construct an equation that models the repayment of a high value loan. Such as a mortgage. The loan is based on compound interest with a monthly calculation and repayment cycle. The site system forcing me to add a question mark: ?
Set the monthly repayment as R, the annual percent interest (apr) as T% and the initial principle sum as #P_0#
This question is set so that I may demonstrate some mathematical processes.
Set the monthly repayment as R, the annual percent interest (apr) as T% and the initial principle sum as
This question is set so that I may demonstrate some mathematical processes.
2 Answers
Let the number of years be
Let the count of calculation cycles be
Given that the initial principle sum is
Set the adjusted principle after the 1st cycle as
Set the adjusted principle after the 2nd cycle as
Set the adjusted principle after the 3rd cycle as
The interest for 1 year is
So splitting this over each month gives
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Repeating this process but with full substitution
..........................................................................
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Using the same approach we end up with:
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Let
Factor out the
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From this it is obvious that ( hate that phrase!)
For any n we have:
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With full explanation this is a big solution so I am splitting it
See Solution part 1 first
Following on from:
Set as
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Note that at the completion of paying off the loan
To take this further we need to determine the sum of the series within the brackets.
set
Then
Factor out the
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Substitute
But
To determine the different values set
Do not forget that