Use the information to answer the following two questions You plan to retire in 30 years. .You project that you will live another 20 years after...

I disagree... You are right that B is correct.  Here's how to go about it.

First, you need to figure out how much you will need at the beginning of your retirement (so that you can draw money out at $50,000 per year and not run out until you die, 20 years after retiring).

The formula for that is:

PVA = ANN* {1-[1/(1+i)^n]}/i

ANN is your annuity -- the $50,000 that you want each year, i is your interest rate and n is how many years you need the annuity.

So: PVA = 50,000*{1-[1/(1.05)^20]}/.05

1.05^20 is 2.653298; 1 divided by that is .376889.  When you subtract that from 1 you get .623111.  Divide that by .05 and you have 12.46221.

So then 50,000*12.46221 = 623,110.5171

So that's the lump sum you need when you retire.

And now you have to figure out how much you need to invest each year (at 5% compounded annually) to get to that $623,110.52 number.

The formula for that is:

ANN = FVA*i/(1+i)^n - 1

Again, i is .05 and n is the number of years you have to save, in this case 30.

By plugging in info you gave and the number we got above:

ANN = 623110.5171*.05/(1.05^30)-1

which gets us

31155.52586/4.321942375-1

which gets you

9378.7, which rounds to 9379

Sorry, don't have a financial calculator, but that's the thought process and the formulas...