A person borrows Rs. 1,00,000 from a bank at 10% per annum simple interest and clears the debt in five years. If the instalment paid at the end of the first, second, third and fourth years to clear the debt are Rs. 10,000, Rs. 20,000, Rs. 30,000 and Rs. 40,000, respectively, what amount should be paid at the end of the fifth year to clear the debt?

$$\eqalign{ & {\text{Interest at the end of }}{{\text{1}}^{{\text{st}}}}{\text{ year}} \cr & = \frac{{1,00,000 \times 10}}{{100}} \cr & = 10,000 \cr & {\text{Paid amount}} = 10,000 \cr & {\text{Rest amount}} \cr & = 1,10,000 - 10,000 \cr & = 1,00,000 \cr & {\text{Interest for }}{{\text{2}}^{{\text{nd}}}}{\text{ year}} = 10,000 \cr & {\text{Amount paid}} = 20,000 \cr & {\text{Remaining amount}} \cr & = 1,10,000 - 20,000 \cr & = 90,000 \cr & {\text{Interest for }}{{\text{3}}^{{\text{rd}}}}{\text{ year}} = 9,000 \cr & {\text{Amount paid}} = 30,000 \cr & {\text{Remaining amount}} \cr & = 99,000 - 30,000 \cr & = 69,000 \cr & {\text{Interest for }}{{\text{4}}^{{\text{th}}}}{\text{ year}} = 6,900 \cr & {\text{Amount paid}} = 40,000 \cr & {\text{Remaining amount}} \cr & = 75,900 - 40,000 \cr & = 35,900 \cr & {\text{Interest for }}{{\text{5}}^{{\text{th}}}}{\text{ year}} \cr & = \frac{{35,900 \times 10}}{{100}} \cr & = 3,590 \cr & {\text{Amount paid at the end of }}{{\text{5}}^{{\text{th}}}}{\text{ year}} \cr & = 35,900 + 3,590 \cr & = 39,490 \cr} $$