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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