An investor accumulates a fund by making payments at the beginning of each

month for six years. Her monthly payment is $50$ for the first two years, $100$ for

the next two years, and $150$ for the last two years. At the end of the seventh year

the fund is worth $10,000.$ The annual effective interest rate is i and the monthly

effective interest rate is j$.$ Find the equation of value for this fund accumulation.