Joe won a lottery jackpot that will pay him $12,000 each year for the next ten years?

Question

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?

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.



Thank you for you help!

Answer 1

The answer can be arrived by using the following formula.
Amount required now= C/r(1-(1/1+r)^t), where
C= Annuity payment= 12000
r=Interest rate=12%=0.12
t=time=10 years
So amount invested will get interest and at the end of the year the amount remaining is initial amount+interest earned-amount paid out
Thus Amount= $67802.67

To verify you can check the answer as below?(starting with the amount as given by above answer)

C r time Amount required
12000 0.12 10 67802.67634
Amount at start of year Interest Total Payout Left at end of year
67802.7 8136.3 75939.0 12000.0 63939.0
63939.0 7672.7 71611.7 12000.0 59611.7
59611.7 7153.4 66765.1 12000.0 54765.1
54765.1 6571.8 61336.9 12000.0 49336.9
49336.9 5920.4 55257.3 12000.0 43257.3
43257.3 5190.9 48448.2 12000.0 36448.2
36448.2 4373.8 40822.0 12000.0 28822.0
28822.0 3458.6 32280.6 12000.0 20280.6
20280.6 2433.7 22714.3 12000.0 10714.3
10714.3 1285.7 12000.0 12000.0 0.0

Answer 2

It's very simple and you're wrong I'm afraid.

His prize is $12000 per year. Let's assume that it all represents interest. So if they iivest $100000 that will produce $12000 each year for ten years then at the end they gert the $100000 back and he gets the $12000 pa interest.

Answer 3

It relies upon on how activity is compounded. If it is compounded continuously, then you definately can use the formulation A=Pe^(rt), the place P is the preliminary quantity invested, r is the activity fee (for that reason 0.12), t is the quantity of time for which the money is invested, in years, and A is the comprehensive stability after t years, alongside with activity.

Answer 4

The answer is 67,802.68. If you use a financial calculator doing these problems becomes MUCH easier. I used a hp 10B II. If you use one of these it is just a matter of entering the right information.

Answer 5

You forgot to figure in what the government will take...
Joe will have $50 when it's all done. :)