Smith, age $65,$ is evaluating three temporary life annuities, each of which provides annual payments. For each annuity, the last payment is made at age $75.$ The first annuity pays $$5,000$ at age $66$; subsequent payments decrease by $$500$ per year. The present value of this annuity is $$14,000.$ The second annuity pays $$1,000$ at age $65$; subsequent payments increase by $$1,000$ per year through age $75.$ The present value of this annuity is $$21,000.$ The third annuity pays $$1,000$ each year beginning at age $65$ and continuing to age $75.$ The present value of this annuity is P$.$ Determine P$.$