A bank offers a nominal interest rate of $5\%$ p$.$a$.$ compounded monthly.

One of its clients is planning to retire in $10$ years and has decided to put a fixed

amount $D$ in the bank at the beginning of each of the months before retirement,

so that the client is able to withdraw $1000$ at the beginning of each month for

the following $20$ years. At the time when the client starts to receive the monthly

payments, the nominal interest rate compounded monthly increases to $10\%$ p$.$a$.$

How large does $D$ need to be$?$