Joe won a lottery jackpot that will pay him $12,000 each year?

Question

My initial answer is this.....But I'm not sure if I did it right. I saw somone else do it where you increase the interest every year; however it is saying how much do they invest toaday. So I'm all confused.

Winning prize of $12,000 x 10yrs = $120,000
Interest per year @12% = $1,440 x10 yrs = $14,400
The total investment over the next ten years paid out for Joe’s winning lottery is $134,400.

Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years. If the market interest rates are currently 12%, how much does the lottery have to invest today to pay out this prize to Joe over the next ten years?

Answer 1

No, you have it backward. It is called an annuity calculation.
One way of looking at it is: How much money today to give out 12,000 a year for ten years? Suppose an interest rate of 12% was available (wow). If we borrowed it All today and paid it all at the end, your calculation would be right. But after a year, we don't have to pay interest on the 12,000 just paid and so on for 10 years.
So lets burrow less money and arrange things so that at the beginning of the last year we have exactly enough money so the interest on it will give us 12,000 to pay out at the end of the year. (1.12x = 12000, x = 10714.29) The 1 285.71 in interest exactly fills out the final payment. Now do that for every year back to the beginning and we can determine the Net Present Value (NPV) of the annuity. Excel gives us exactly that function plus one called PV (Present Value) NPV allows diffferent payments each year whilce PV calculates for the same In this case, using PV and a payment at the end of each year,* $67,802.68 is required now to pay the reward. Which is why you are given a choice of annual payments or a smaller lump sum.
* This can get tricky because Lottery payments usually start right away, so the first payment earns no discounting interest. The Excel PB function allows payment at the beginning or end of the periods. If you are doing it manually, you have to remember only 11 more payments if at the beginning.
** Answer number 1 is doing what the winner would acummulate.

Answer 2

Since I don't have the text of the question I'm not precisely sure, but here's my guess.

Joe has a lottery jackpot that will pay him $12k/year.
It accrues interest at a rate of 12% per year.
Principal ($12k) plus interest ($1,440) at the end of Year 1 is $13,440.

However, the interest is 12% per year on ALL the money, not just on the $12k/year, so the calculations for Year Two look like this:

Starting balance of $13,440
plus yearly payout $12,000
$25,440 is the amount that earns interest in Year Two.
* 1.12 (itself plus twelve percent) = $28,492.80 at the end of Year Two, and so forth. You keep doing that...

Starting balance of $28,492.80 plus 12k = 40,492.80 @ 12% interest leaves an end balance of $45,351.94 at the end of year three.

You'd keep doing until you'd calculated 10 years worth.
You have to keep compounding the interest because the amount of money there at the end of each year includes the interest paid that year, which will in turn accrue future interest. Calculating 10 years worth of interest based on the starting value will show significantly less money than it should.

You can see already that compounding the interest is going to make the value significantly more than your original answer, which would have put Joe's value at the end of year three at $40,320, already $5k less than the compound interest value.

Hope that helps! If the question asks for something different, please repost it. Good luck!

Answer 3

I think what happened here without knowing any more details is:
Joe won $120,000 in a lottery.
If he collected the full amount in one year his income tax bracket would be so high he might have to give 1/2 or more {$60,000} to his state and federal government for taxes.

So Joe decided to take the $12,000 a year pay-off option instead of the full amount and use the $12,000 for living expenses.......And Quit His Job!

If he decided to let the winnings ride at a promised 12% annual rate of return, by re-investing the original $120,000 for ten years, {after a certain age (70?) the tax bite goes way down} compounding the interest, for $120,000 he probably would end up with well over $300,000.

.......But how do you figure in inflation?

At an annual "REAL" inflation rate of 5% his original $120,000 would only buy about $150,000 worth of goods. {5X10=50%!!! 50% of $300,000 is $150,000}

At an annual real inflation rate of 6% he would break even===$120,000 in purchasing power after 10 years. {6X10=60%! 60% of 300,000 is $180,000! $300,000-$180,000=$120,000}

Answer 4

it incredibly is extremely easy and you're incorrect i'm afraid. His prize is $12000 according to 365 days. enable's anticipate that all of it represents activity. So in the event that they iivest $one hundred thousand which will produce $12000 each and each 365 days for ten years then on the tip they gert the $one hundred thousand returned and he gets the $12000 pa activity.

Answer 5

Hey Joe, could a borrow a couple thou?