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.
<pre>It takes 15 months to pay off $1,500, @ $100 per month.
Interest of 1% ({{{"12%"/12}}}) 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 1<sup>st</sup> interest payment of <s>$140</s> $14 ($1,500 - 100) * .01 (1%), 
and decreases by <s>$10</s> $1 each month thereafter, for 15 months, with last being 0, since the remaining $100 will be paid then. 
We then get: {{{matrix(4,3, S[n], "=", (n/2)(2a[1] + (n - 1)d), 
S[15], "=", (15/2)(2(14) + (15 - 1)- 1),
S[15], "=", (15/2)(28 - 14),
S[15], "=", (15/2)(14))}}}
Sum of 15 monthly interest payments, or {{{highlight_green(matrix(1,5, S[15], "=", 15(7), "=", highlight("$105")))}}}

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!</pre>