Question 1201478
.
You win the lottery and get $100 per day for 25 years. 
Assuming a yearly interest rate of 6%, compounded daily, 
how much is the series of payments worth in today's dollars?
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<pre>
This saving plan of depositing $100 per day for 25 years at a yearly interest rate of 6%, 
compounded daily, is called an ORDINARY ANNUITY plan.


There is a formula to calculate the total amount which the plan generate at the end.


This formula is

    f = {{{p * (((1 + r) ^ n-1)/r)}}},


f is the future value
p is the daily payment
r is the interest rate per time period
n is the number of time periods.


In your problem:


time periods are days.
p = 100 dollars  
r = 0.06/365 per day (counting 365 days in a year)
n = 25*365 = 9125 days in 25 years


formula becomes f = {{{100*(((1 + 0.06/365)^9125-1)/((0.06/365)))}}} = 2,117,691.45 dollars (rounded).


Now, your problem asks, what amount should be deposited one time today
on the 25 years account giving 6% interest rate annually and compounded daily,
in order for to get the same total of $2,117,691.45 at the end of 25 years?


To determine it, we write this equation for the unknown principal amount P

    2117691.45 = {{{P*(1+0.06/365)^9125}}}.


From this equation we get the <U>ANSWER</U>

    P = {{{2117691.45/(1+0.06/365)^9125}}} = 472579.09.


So, in today's dollars, your winning is EQUIVALENT to  $472,579.09.    <U>ANSWER</U>
</pre>

Solved.


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On &nbsp;Ordinary &nbsp;Annuity saving plans see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Sequences-and-series/Ordinary-Annuity-saving-plans-and-geometric-progressions.lesson>Ordinary Annuity saving plans and geometric progressions</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Sequences-and-series/Solved-problem-on-Ordinary-Annuity-saving-plans.lesson>Solved problems on Ordinary Annuity saving plans</A> 

in this site.


The lessons contain &nbsp;EVERYTHING &nbsp;you need to know about this subject, &nbsp;in clear and compact form.



On discretely compounded accounts, &nbsp;see the lessons

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/percentage/lessons/Compound-interest-percentage-problem.lesson>Compound interest percentage problems</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/logarithm/Problems-on-discretely-compound-accounts.lesson>Problems on discretely compound accounts</A> 

in this site.



Happy learning &nbsp;(&nbsp;!&nbsp;)