Felicity has just commenced work and is investigating superannuation funds.

Question

She calculates that she will need $1 000 000 in her fund when she retires in 40
years. She finds a fund guaranteeing to pay interest on each deposit at a rate of
6% per annum compounded monthly.
She intends to deposit $M into the fund at the beginning of each month for the
first 25 years (300 months). For the remaining 15 years (180 months), she will
deposit $2M into the fund.
Find the value of M.