An investment of P$25,000,$ producing an income of P$750$ each $6$ months, is left to a $12-$year$-$old child. The child is allowed one half of the income for expenses, while the other half is invested for him at $4\%$ compounded semiannually. These accumulations, together with the principal invested, become the property of the child on his twenty$-$first birthday. What is the value of this legacy on that date?