Mary deposits $1000$ into a fund at the beginning of each year for $10$ years. At the end

of $15$ years, she makes an additional deposit of X$.$

At the end of $20$ years, Mary uses the accumulated balance in the fund to buy a

perpetuity$-$immediate with annual payments of $2000$ per year for $10$ years, and $1000$

per year thereafter.

Interest is credited at an annual effective rate of $5\%.$

Calculate X$.$

Correct answer is $4865\mathrm{.}13,$ looking for a worked out solution, studying for an exam