Timothy buys furniture to the value of \(R 10000\). He borrows the money on 1 February 2010 from a financial institution that charges interest at a rate of 9,5% per annum compounded monthly. Timothy agrees to pay monthly instalments of R450. The agreement of the loan allows Timothy to start paying these equal monthly instalments from 1 August 2010.

(a) Calculate the total amount owing to the financial institution on 1 July 2010.

(b) How many months will it take Timothy to pay back the loan?

(c) What is the balance of the loan immediately after Timothy has made the 25th payment?

(d) What is the final payment if it is made at the end of the month?