Let’s try to solve this problem together.👍
First, we need to find the amount of each of the first three installments. Since they are 1/4 of the principal, we can divide 1040 by 4 to get 260. So, A pays 260 rupees each year for the first three years.
Next, we need to find the amount of interest that accumulates on the loan over the four years. Since the interest rate is 5%, we can multiply 1040 by 0.05 to get 52. This is the interest for one year. To find the total interest, we need to add up the interest for each year, taking into account that the principal decreases as A pays off some of the loan.
The interest for the first year is 52 rupees, since the principal is still 1040. The interest for the second year is 52 - (260 x 0.05) = 39 rupees, since the principal is now 1040 - 260 = 780. The interest for the third year is 52 - (520 x 0.05) = 26 rupees, since the principal is now 1040 - 520 = 520. The interest for the fourth year is 52 - (780 x 0.05) = 13 rupees, since the principal is now 1040 - 780 = 260.
The total interest is 52 + 39 + 26 + 13 = 130 rupees.
Finally, we need to find the amount of the last installment. This is equal to the remaining principal plus the total interest. The remaining principal is 1040 - (260 x 3) = 260 rupees. The total interest is 130 rupees. So, the last installment is 260 + 130 = **390 rupees**.
Therefore, A pays **390 rupees** in the last installment.