You won the lottery and will collect your winning in the following $3$ installments. Your payments will come at the end of the year.

Assume the appropriate discount rate is $10\%$ compounded annually.

Year $1$: $$1,000$

Year $2$: $$2,000$

Year $3$: $$3,000$

$$

What is the present value of your cash flow?

$$

$$6,000$

$$5,455$

$$4,816$

$($Please DO NOT show me excel computations. Please show me calculations through equations. If possible, financial calculator computations would be appreciated as well.$)$