Let's break down the problem into steps to solve it:
Calculate the interest for the first 2 years:
The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.
In this case, P = Rs 45,000, r = 10%, n = 1 (compounded annually), and t = 2 years.
So, A = 45000(1 + 0.1/1)^(1x2) = Rs 59,049
Therefore, the interest for the first 2 years is Rs 59,049 - Rs 45,000 = Rs 14,049
Calculate the remaining principal:
Ram paid one third of the principal at the end of 2 years, which is (1/3) x Rs 45,000 = Rs 15,000.
So, the remaining principal after 2 years is Rs 45,000 - Rs 15,000 = Rs 30,000
Calculate the interest for the next 2 years:
Since Ram paid off the remaining principal and interest at the same rate at the end of the next 2 years, the interest rate will still be 10%.
So, the interest for the next 2 years will be:
A = 30,000(1 + 0.1/1)^(1x2) = Rs 39,690
Therefore, the interest for the next 2 years is Rs 39,690 - Rs 30,000 = Rs 9,690
Calculate the total amount Ram paid at the end of 4 years:
To clear his debt, Ram paid the remaining principal (Rs 30,000) and the interest for the next 2 years (Rs 9,690).
So, the total amount he paid at the end of 4 years is Rs 30,000 + Rs 9,690 = Rs 39,690.
Therefore, Ram paid Rs 39,690 at last to clear his debt.