Question

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.

Answer 1

After 40 days the prize money has still
not been won. Calculate the total amount donated to charity
(i) if Model 1 is used,
(ii) if Model 2 is used.

Answer 2

I think I got it!!:) U might wanna check this answer before you put it in....
(i) if Model 1 is used,
Charity donated = (5/100)[(40/2)(1000 + 40000)] = 41000 Answer
(ii) if Model 2 is used.
Charity donated = (5/100)[1000{1 -- 1/10^40} (1 -- 1/10) = 1111 1/9

Answer 3

i) n/2(2a1+(n-1)d)*5/100=40/2(2*1000+(40-1)*1000)*5/100=41000. Part i, your answer for Part i is correct but for Part ii) your answer is incorrect.

Answer 4

That's why I said u might want to check with someone else!!:)

Answer 5

okay thanks for your time :)

Answer 6

Welcome!!:)

Answer 7

Model 2: Money is increased by 10%.
1000*10/100=100, 100+1000=1100. the formula to get the second term of the GP is ar. 1000r=1100. r=1.1
The series are 1000,1100,1210,1331...
(1000(1.1^40-1)/1.1-0.1)*5/100=22129.62