SOLUTION: Dianne won a lottery prize of $200,000. She invested the entire amount and expects a yearly return of 10% per annum compounded monthly on her investment. Dianne will receive 150 e

Question 1114200: Dianne won a lottery prize of $200,000. She invested the entire amount and expects a yearly return
of 10% per annum compounded monthly on her investment. Dianne will receive 150 equal monthly
payments with the first payment due to be paid to her in exactly 2 years. Find the size of the monthly
payments that Dianne will receive.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

At the end of the first 2 years period Dianna's account will be


 = 244078.20  dollars.



Starting from this day, she will receive 150 equal monthly payments.


In other words, she will withdraw 150 equal monthly amounts from her account.


But the account still will compound monthly the rest of the amount in her account.

    The problem did not state it in the condition, but it is how I interpret it.


It works as the ANNUITY DUE saving plan with the negative deposit
    (see the lesson  Annuity Due saving plans and geometric progressions  in this site).


Let x be this unknown amount Diana withdraw every month.


The equation to find x is THIS:


244078.20 = ,    or, equivalently


244078.20 = ,


244078.20 = x*85.08575.


Hence,  x =  = 2868.61 dollars.


Answer.  The size of the monthly payments that Dianne will receive is  2868.61 dollars.

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