This question essentially appears to be asking for the monthly payment amount earning 13.4%, compounded monthly, required to achieve $1,000,000 in ten years. The basic components of this type of problem are: present value (PV), future value (FV), payment (PMT), interest rate (i) and number of periods (n). Assigning known amounts to these variables:
PV = 0 (beginning balance in the mutual fund)
FV = $1,000,000
PMT = unknown
i = 13.4% / 12 = 1.116667% = 0.01116667 (interest rates are given in annual terms; however, since it is compounded monthly, we divide by 12 months to get the interest rate on a monthly basis)
n = 10 * 12 = 120 (10 years * 12 months per year = 120 months, again because interest is compounded on a monthly basis)
At this point, you could use a financial calculator to input the known variables and solve for the unknown (PMT) or use the PMT function in Excel. If solving manually, the formula is as follows:
PMT = (FV*i) / ((1+i)n - 1)
PMT = (1,000,000*0.01116667) / ((1+0.01116667)120 - 1) = 11166.67 / (1.01116667120 - 1) = 11166.67 / (3.790788 - 1) = 11166.67 / 2.790788 = 4,001.25
Therefore, you would need to invest $4,001.26 (approximately, due to rounding) each month, yielding 13.4% compounded monthly to have $1,000,000 after 10 years.
Note: I have assumed that the monthly payments will be made at the end of each month (called an ordinary annuity) as opposed to the beginning of each month (called an annuity due). The annuity due scenario would require a slightly different formula.