Setting personal motives aside interest rate calculation is a valid consideration on making a decision of cash vs annutiy for lottery winnings. Another consideration not mentioned is that the long term annuity of 20 or more years offers no protection from inflation. A lump sum cash payment can be invested in ways that can minimize the effects of inflation on the purchasing power of the lottery winnings. Personally I would take a cash sum where I would have control to adjust wealth protection strategies vs being subject to the unknowns of future inflation cycles and tax policies.
I presume you’re commenting on this column (“If I win the lottery, should I ask for a lump sum or an annuity?”)
Sure, the lump sum CAN be invested so as to outpace inflation… but will it?
Unlike most people, I am cognizant of the fact I am not a financial/investing wizard. Sure, I might get a slightly lower rate of return, but I’ll still be disgustingly rich either way. I’d be tempted to go for the annuity. That way, I can live on some and invest some every year, and if I screw up one year well, I didn’t blow it all at once.
I’m scheduled* to win the powerball this Saturday. I figure I’ll give $35M to charity, $118.125M to the feds for taxes, place $39.375M in two separate checking accounts for me and kaylasmom, set aside $81M in 90 shares of $900K for distribution to family members, invest $75.4M in tax-free municipal bonds at 4%, and take the family on vacation this summer on the remaining $1.1M.** I don’t need to GROW the damn fortune. Hell, I could put $75.4M under the mattress and spend $14.5K per week and it would take me a hundred years to get through it.
Were the cash value payout to be significantly lower, I’d probably shell out a few bucks to a professional to manage it for me.
*Scheduled my ME, that’s who. I wrote it right there in my Day-Planner. Also, I called “dibs.”
**You know, unless the estimated cash value changes again before tomorrow night. Then I’ll have to recalculate.
Well, the Powerball annuity is set up to account for inflation. For the recent $600,000,000 annuity, the initial payment will be $10,698,059.48 and will increase by 4% each year for 29 years for a final payment of $33,363,518.73 in the year 2042
You might like to borrow money for some purposes, even though you could pay cash. For example, you might well be able to get a greater ROI than current mortgage rates, so it would make sense to purchase a house with a mortgage even though you have the cash.
This can be a problem for people who’s only income comes from investments. Or from profit from businesses they own. Lenders want to see a steady paycheck. No paycheck, no loan.
An annuity is counted as income by most lending institutions. So going for the annuity might improve your credit worthiness.
You just won $300+ million after taxes. What the heck do you need credit for? 
I know, I know…lesser amounts. But annuities are usually only on amounts over $1 million. If you still need to borrow money, you’re spending too much.
I’m sure if you have $300M in the bank, that bank will be willing to give you a line of credit. I’m sure assets can cover credit.
I guess before you can decide whether you want a lump sum payment or take the annuity, you’ve got to first buy a lottery ticket.
I play the lottery every week by picking ten sets of numbers and not buying any tickets. When my numbers don’t come up, I total up the amount of money I didn’t waste on buying tickets and consider it my winnings.
There are other ways to win the lottery, but you should try not to get caught.
Sorry for reviving a somewhat old thread, but i see something that appears to be a big mistake in this column.
I’m talking about this part:
" I find that if we start with a cash value of $500,000 and expect to wind up with $1,000,000 after 20 years (in other words, the equivalent of a $50,000 annuity), the underlying annual interest rate has to be 8.92%."
Either I’m not seeing something, or Dex calculated that wrong. We can count capital at the end of the investment period in several ways, e.g. with annual, monthly or daily interest compounding. In these cases we would wound up with most money with the daily type, but even assuming that interest compounding takes place only once a year, we get to: 500,000*(1.0892)^20 ~= 2,761,000.
And even assuming that no interest compounding takes place we get 500,000*(1 + 0.0892*20)~= 1,392,000.
As I see it, the correct way to count this is to take the ratio of capital we want to get at the end to starting capital(in this case 2:1), and from this calculate needed interest rate. 1,000,000 = 500,000*(1+n)^20, where n is interest rate. (this is assuming annual interest compounding). We get 1+n = (1,000,000/500,000)^(1/20) = 2^(1/20) ~= 1,0352. So n = 3,52%.
Am I right, or I don’t know something about finance or grade school maths?
I have really bad news for you, lucjan, my calculations are coming up with the same answers as yours. I’m using a spreadsheet with it’s preprogrammed functions. Another way to look at this is that: On the come-out roll, the shooter has 8 of 36 winners, 4 of 36 losers, which gives an overall positive 4 of 36, or 11% return for the shooter. Of course that’s average return on investment, your results may differ.
It’s not 500K * (1+i)[sup]20[/sup], that would be if you simply invested the $500K and then waited 20 years and took out all the capital. My assumption was that you’re taking out $50K each year. It’s an annuity, not simply an investment.
Thus, the formula is something like (dropping 000s and using i for interest and n for number of years – typical financial calc symbols): $500*(1+i)[sup]20[/sup] - 50*(1+i)[sup]19[/sup] - 50*(1+i)[sup]18[/sup] - … Each year, the capital sum (the $500K) is diminished by $50K that you take out as the annuity. OK?
Hi C K Dexter Haven!
I see what you had in mind. Just one note, maybe it will be useful for others reading this thread:
I assume you got that formula from something like that -
FIRST YEAR: starting capital: 500, return of investment: 500 * i (=8,92%) = 40,14, money withdrawn: 50, yielding 490,14 capital for next year
SECOND YEAR: starting capital: 490,14, return of investment: 490,14 * 8,92 % = 33,30; money withdrawn: 50, yielding 473,44 for next year
etc.
Getting it to 20 years results in a formula given by you. Using it we should end up in 0$ invested at the end of year 20 and 1000 withdrawn over 20 years (*). Right?
But using 500 as starting capital results in 1000$ withdrawn over the course of investment, and ca. 253 left for further investments. For assumption (*) to be true interest rate should be about 7,44%.
I understand that writing this column you assumed that first withdrawal takes places at the beginning of the first year, resulting in 450$ in starting capital. In this case interest rate needed to get to 0 “in a bank” and 1000 “in pocket” at the end is in fact about 8,92%. It all makes perfect sense now! Thanks.
You don’t even realize how happy I am to know that I didn’t find such a simple mistake in Straight Dope 
Keep up the good work!
ditto
Yes, sorry, lucjan, I assumed the first $50K was taken out at the beginning of year 1 (to live on.) Thus, you start with $500 - 50 = 450.
That earns interest at i% per year, so one year later you have 450(1+i).
You take out 50 to live on, so you have 450(1+i)-50
One year later, at end of year 2, you have (450(1+i)-50)(1+i) = 450(1+i)[sup]2[/sup] - 50(1+i)
You take out 50 to live on, so you have {450(1+i)[sup]2[/sup] - 50(1+i)}-50. That earns interest for the year, so {450(1+i)[sup]2[/sup] - 50(1+i) - 50}(1+i) = 450(1+i)[sup]3[/sup] - 50(1+i)[sup]2[/sup] - 50(1+i). Continuing for 20 years, the amount remaining should be:
450(1+i)[sup]20 - 50(1+i)[sup]19[/sup] - 50(1+i)[sup]18[/sup] - … - 50 = 0. And solve for i.
My formula in post #12 above was incorrect, and not what I used in the staff report. (I did say “something like” because I didn’t remember whether I’d used beginning of year or end of year for withdrawals. Beginning of year makes most sense, but I wasn’t thinking clearly this morning.)