CAIE P1 2011 June — Question 8

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2011
SessionJune
TopicSequences and Series

8 A television quiz show takes place every day. On day 1 the prize money is \(
) 1000$. If this is not won the prize money is increased for day 2 . The prize money is increased in a similar way every day until it is won. The television company considered the following two different models for increasing the prize money. Model 1: Increase the prize money by \(
) 1000$ each day.
Model 2: Increase the prize money by \(10 \%\) each day.
On each day that the prize money is not won the television company makes a donation to charity. The amount donated is \(5 \%\) of the value of the prize on that day. After 40 days the prize money has still not been won. Calculate the total amount donated to charity
  1. if Model 1 is used,
  2. if Model 2 is used.