You win $$38,000$ in the state lottery to be paid in two installments: $$19,000$ now and $$19,000$ one year from now.

A friend offers you $$36,000$ in return for your two lottery payments. Instead of accepting your friend's offer, you take out a one$-$year loan at an interest rate of $8\mathrm{.}25\%$ per year, compounded annually. The loan will be paid back by a single payment of $$19,000($your second lottery check$)$ at the end of the year.

What is the present value of $$19,000$ one year from now?

Present value $=$$

Which is better, your friend's offer or the loan?