SOLUTION: Here is my problem...For the past three years, you've spent $12 each week on lottery tickets, averaging $624 per year. Instead of buying tickets, you now decide to deposit $624 at

Algebra ->  Finance -> SOLUTION: Here is my problem...For the past three years, you've spent $12 each week on lottery tickets, averaging $624 per year. Instead of buying tickets, you now decide to deposit $624 at      Log On


   

Question 473741: Here is my problem...For the past three years, you've spent $12 each week on lottery tickets, averaging $624 per year. Instead of buying tickets, you now decide to deposit $624 at the end of each year into an annuity. How much money will you have in this annuity after 20 years if it pays 7% interest, compounded annually? How much of this is interest?
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Ok at the end of 1st year you deposit 624 but then it sits there and earns interest for 19 years, the 624 you deposit at end of 2nd year earns interest for 18 years and so on...
Then the future value of the first deposit is 624%2A%281.07%29%5E19
By adding up all the deposits you obtain a geometric sequence:
624(1 + 1.07 + ...+(1.07)^19)
The sum of a geometric sequence is S+=+a1%281-r%5En%29%2F%281-r%29
where a1 is the first term, r is the common ratio, n is the number of terms
S+=+624%281%29%281-%281.07%29%5E20%29%2F%281-1.07%29
S+=+624%28-2.8697%29%2F%28-.07%29
S+=+25581.19
Now the amount you actually paid into it is 624*20 = 12,480, the difference is interest earned.
25581.19+-+12480+=+13101.19
Therefore after 20 years, you will have $25,581.19 of which $13,101.19 is interest.