Jean$-$Rene wants to make a lump$-$sum deposit today such that at the end of every three months for the next five

years he can receive a payment starting at $$2,500$ and increasing by $1\%$ each time thereafter. At the end of the

term, an additional lump$-$sum payment of $$10,000$ is required. If the annuity can earn $8\mathrm{.}75\%$ compounded

semi$-$annually, what lump sum should he deposit today?