Charlie has won the lottery and he just turned $14$ years old $($today is his birthday$).$ However,

by law the lottery is not allowed to pay out money until a person is at least $18$ years old.

Nevertheless, in the meantime, the winnings can be invested in an interest earning trust fund.

Charlie hires a consultant to define the investment strategy and this financial consultant

recommends that Charlie should invest the money in an equity fund, which is expected to

generate an $8\%$ annual effective return for Charlie.

The consultant is charging Charlie a one$-$time $1\%$ fee of the total winnings, payable

immediately when Charlie is $14,$ before the remainder of the money is invested in the trust.

Charlie is told he can expect to receive payouts of $2\mathrm{.}500$$ from the trust each month, with the

first payment being made on his $18$th birthday. Additionally, the payments will increase with

inflation annually, by $2\%.$ So$,$ there are $12$ equal payments in year $1$ of $2\mathrm{.}500$$ $($starting when

Charlie turns $18),$ the next $12$ equal payments are of $2\mathrm{.}500*(1,02)$$ $($starting when Charlie turns

$19),$ year $3$ payments are $2\mathrm{.}500*(1,02)2$

and so on$.($PAYMENTS ARE MADE MONTHLY,

BUT THEY INCREASE IN VALUE ONLY ONCE A YEAR...$).$

Charlie has won enough money for this payment scheme to last for exactly $25$ years, so he will

receive the last payment exactly one month before his $43$rd birthday.

How much did Charlie win in the lottery, how much does the consultant receive and how much

gets invested in the trust fund??