A father decided to buy a house for his family for \(\mathrm{R} 800000\). He agreed to pay monthly instalments of R10 000 on a loan which incurred interest at a rate of \(14 \%\) per annum compounded monthly. The first payment was made at the end of the first month.

(a) Show that the loan would be paid off in 234 months.

(b) Suppose the father encountered unexpected expenses and was unable to pay any instalments at the end of the \(120^{\text {th }}, 121^{\text {st }}, 122^{\text {nd }}\) and \(123^{\text {rd }}\) months. At the end of the \(124^{\text {th }}\) month he increased his payment so as to still pay off the loan in 234 months by 111 equal monthly payments. Calculate the value of this new instalment. You may assume that the balance outstanding after the \(119^{\text {th }}\) payment has been made is R629 938,11 .