SOLUTION: Uncle Bob's will states you will recieve $1000 on your 21st birthday. Then every month afterward you will recieve 95% of the amount you recieved the previous month. When will you r

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Question 196057: Uncle Bob's will states you will recieve $1000 on your 21st birthday. Then every month afterward you will recieve 95% of the amount you recieved the previous month. When will you recieve an amount less than 1 cent? (which month after birthday) What will be the total you have recieved?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!

Since each month you get 95% of what you got the month before, on the 1st month after your birthday, you would get .95*1000. On the second month, you would get .95*.95*1000, and so on. On the nth month you would get:



So we want to solve for n when



So:









So, at month 224 you would get a little more than $0.01 and in month 225 a little less than $0.01. Hence, the answer to the question posed is month 225 if your birthday was in month 0, at which time you would be 39 years, 9 months old.

The total amount received after you received the month 225 payment is a geometric series with a common coefficient of 1000 and a common ratio of 0.95. The sum of a geometric series that starts at term 0 is given by:



So:



Start punching that calculator.

John