Question
On 1 January 2001 Amy put into a bank account,
and on the first day of each subsequent month she put in
more than in the previous month. Thus on 1 February she put in into
the account and on 1 March she put in into the account, and so on.
The account pays no interest.
(i)
On what date did the value of Amy's account first become greater than
[5]
On 1 January 2001 Bob put into an investment account, and on the
first day of each subsequent month he put another into the account. The
interest rate was per month, so that on the last day of each month the
amount int the account on that day was increased by
(ii)
Use the formula for the sum of a geometric progression to find an expression for the value
of Bob's account on the last day of the month (where January 2001 was the 1st month,
February 2001 was the 2nd month, and so on). Hence find in which month the value of Bob's account first became
greater than
[5]
(iii)
Bob wanted the value of his account to be on 2 December 2003.
What interest rate per month, applied from January 2001, would achieve this?
[3]