If I use the formula using HP, I am getting 175,1311.67. How is C correct? I also did not understand how is this scenario possible without any PV. Do you know how PV can miss here? Consider a 10-year annuity that promises to pay out $10,000 per year; given this is an ordinary annuity and that an investor can earn 10 percent on her money, the future value of this annuity, at the end of 10 years, would be: A) $175,312. B) $152,500. C) $159,374. D) $110.000. C is correct! N=10; I/Y=10; PMT=-10,000; PV=0; CPT FV=$159,374.
I just typed it on my BA II Plus and got C. With the PV key you can either not type nothing (assumes zero) or type in zero. There is no PV since you did not start with any investment.
10000 * ((1.1^10) - 1)/0.1 = 159.374 … with ANY calculator (that costs more than $5) 
It was my mistake. My calculator was set to Begin mode. Still I have question on other part. My understanding on annuities is banks and insurance companies collect lump sum amount from investor and pays yearly some money for their expenses. Question says “10-year annuity that promises to pay out $10,000 per year”. Does n’t it means Bank or insurance company paying investor? How come they pay if investor does not deposit anything (PV=0)? Or does it means investor is depositing $10,000 year and will get lump sum of $$159,374? Appreciate your help.
Your understanding is correct. The question is just meant to be about present and future values of a stream of annuities. I wouldn’t fret over it too much.