At the start of the academic year, two students planned their savings for a skill-development course. Neha chose a long-term deposit option, while Arjun chose a mixed plan that combined a shorter deposit with a one-year simple-interest reinvestment. Neha deposits Rs. 1,12,000 in a scheme for 4 years at 6% interest per annum, compounded half-yearly. Separately, Arjun deposits a certain amount in the same scheme for 3 years, and then reinvests the entire amount he receives at the end of 3 years for 1 year at 12% simple interest. If the amounts received by both at the end of 4 years are equal, then the initial investment, in rupees, made by Arjun is ______.