
investment
A person 'X' invests 'P' dollars at once. In 7.25 years, if the amount doubles, then what would be the amount in terms of 'P' for 29 years?
So, I see that every 7.25 years we have P+P. Now, 7.25 goes into 29 4 times. Thus, we should have (P+P)^4=(2P)^4=16P^2.
how does this look?

The investment 'P' will double 4 times in 29 years (29/7.25=4). So X would equal P(2^4). It would not equal 16P^2. For example...
Lets say that P equals 3.
3(2^4)=48 != (16(3))^2 = 2304
Besides that you are right, the simplification is off though. :)

A person 'X' invests 'P' dollars at once. In 7.25 years, if the amount doubles, then what would be the amount in terms of 'P' for 29 years?
$\displaystyle 2x = x\cdot p^{7.25} \ \ \ \ \ \ \ 2 = p^{7.25} \ \ \ \ p = \sqrt[7.25]{2} = 1.1 \ \ \ \ $
The amount increased each year for about 10%
$\displaystyle \ \ 1.1^{29} = 16 \ \ \ {After \ 29 \ years \ the \ amount \ will \ increase \ 16 \ times }$
