SOLUTION: Please help me with this problem. Would greatly appreciate your help! You win the lottery and get $100 per day for 25 years. Assuming a yearly interest rate of 6%, compounded da

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Question 1201478: Please help me with this problem. Would greatly appreciate your help!
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?

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~

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 = ,


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 =  = 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 = .


From this equation we get the ANSWER

    P =  = 472579.09.


So, in today's dollars, your winning is EQUIVALENT to  $472,579.09.    ANSWER

Solved.

---------------------

On  Ordinary  Annuity saving plans see the lessons
    - Ordinary Annuity saving plans and geometric progressions
    - Solved problems on Ordinary Annuity saving plans
in this site.

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


On discretely compounded accounts,  see the lessons
    - Compound interest percentage problems
    - Problems on discretely compound accounts
in this site.


Happy learning  ( ! )



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