SOLUTION: A woman borrows $1500, agreeing to pay $100 at the end of each month to reduce the outstanding principal and agreeing to pay the interest due on any unpaid balance at a rate of 12%

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Question 1194388: A woman borrows $1500, agreeing to pay $100 at the end of each month to reduce the outstanding principal and agreeing to pay the interest due on any unpaid balance at a rate of 12% per annum (i.e. 1% per month). Determine the sum of all interest payments.
Found 3 solutions by Theo, MathTherapy, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the loan is 1500.
the payments are 100 at the end of each month.
the interest rate is 12% per year / 12 = 1% per month.
the number of months required to pay off the loan is equal to 16.33301765.
total payments are that * 100 = 1633.01765.
total interest is 1633.01765 minus 1500 = 133.01765.
i used the ti-ba-ii financial calculator.
inputs were:
present value = 1500
future value = 0
payment at the end of each month = -100
interest rate per month = 1%
output was number of months.
let me know if you have any questions.
theo

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
A woman borrows $1500, agreeing to pay $100 at the end of each month to reduce the outstanding principal and agreeing to pay the interest due on any unpaid balance at a rate of 12% per annum (i.e. 1% per month). Determine the sum of all interest payments.
It takes 15 months to pay off $1,500, @ $100 per month.
Interest of 1% () on OUTSTANDING BALANCE is also paid monthly. 
For total interest paid over 15 months, we get the sum of an AP, which begins with a 1st interest payment of $140 $14 ($1,500 - 100) * .01 (1%), 
and decreases by $10 $1 each month thereafter, for 15 months, with last being 0, since the remaining $100 will be paid then. 
We then get: 
Sum of 15 monthly interest payments, or 

Thanks, Tutor @IKLEYN. 
I hastily made the calculations and didn't realize that I calculated 10% interest i/o 1%. I've made the corrections. Thanks again!

Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Tutor @MathTherapy gave a brilliant treatment of the problem and showed the way to solve it.
But his calculations need to be corrected.

I made this correction in the Table below.


     Month	      Debt         Interest (in dolars)
       (end of the month)       paid at the end of the month
----------------------------------------------------------------
      1		      1400		14
      2		      1300		13
      3		      1200		12
      4		      1100		11
      5		      1000		10
      6		       900		 9
      7		       800		 8
      8		       700		 7
      9		       600		 6
     10		       500		 5
     11		       400		 4
     12		       300		 3
     13		       200		 2
     14		       100		 1
     15		         0		 0
---------------------------------------------------------------
                                       sum = 14 + 13 + 12 + . . . + 1 = 105.


ANSWER.  The sum of all interest payments is $105.



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