c2 geometric series hard question

My question has to do with part b of this question:

The question:

A house owner borrows 30,000 from a building society at he start of month 1. At the end of each month, 0.6% interest is charged and added to the debt. On the first day of month 2 and each subsequent month, the borrower pays back £250.

a) Find an expression for the debt outstanding at the end of the month n.

b) Show that, after a year the debt, to the nearest pound is £29113

this is my version...

$30,000 \times 1.006^{12} - \sum_{n=1}^{11}(250 \times 1.006^{n}) = 29113.112$

on the second page of your working you set the lower limit of the sigma sum to 1... this means that you are subtracting £250 on the last day of January, instead of the first day of February ... you are making 12 subtractions during the year instead of 11

thank you very much the bear

Sorry to trouble you again but when i insert you calculation in to the casio fx 991es plus somehow i get a different answer

$30,000 \times 1.006^{12} - \sum_{n=1}^{11}(250 \times 1.006^{n}) = 29381.71804$

$30,000 \times 1.006^{12} - \sum_{n=1}^{12}(250 \times 1.006^{n}) = 29113.112$

i understood that in 12 months the pay back amount is only 11 times thus 11 subtraction. this will mean that for one year there were 12 subtractions which should be wrong right?

is there something wrong which my calculation or is the question the main problem because after a year will be the first day of the new year thus house owner will pay the amount 250 in to the bank.



For part a
Also, does it mean that my answer for the nth them is wrong?

thank you for the help

i worked the calculation as 1st January 2015 to 31st December 2015....

if you get the right answer by making an extra payment then they must be calculating a year as 1st January 2015 to 1st January 2016