If i have 1$ increasing 1% every day for one year, how do i calculate it in %? 100(1+0.01)^365??

If i have 1$ increasing 1% every day for one year, how do i calculate it in %? 100(1+0.01)^365??

$\small{ \begin{array}{|lrcll|} \hline 1. \text{ day} \\ \quad $1 + $1 * 1\ \% \\ \quad = $1 + $1\cdot 0.01 = $1\cdot (1+ 0.01) = \mathbf{$1\cdot (1.01)} \\ \hline 2. \text{ day}\\ \quad $1\cdot (1.01) + $1\cdot (1.01) * 1\ \% \\ \quad = $1\cdot (1.01) + $1\cdot (1.01)\cdot 0.01 = $1\cdot (1.01)\cdot (1+ 0.01) = $1\cdot (1.01)\cdot (1.01) = \mathbf{$1\cdot (1.01)^2 }\\ \hline 3. \text{ day}\\ \quad $1\cdot (1.01)^2 + $1\cdot (1.01)^2 * 1\ \% \\ \quad = $1\cdot (1.01)^2 + $1\cdot (1.01)^2\cdot 0.01 = $1\cdot (1.01)^2\cdot (1+ 0.01) = $1\cdot (1.01)^2\cdot (1.01) = \mathbf{$1\cdot (1.01)^3} \\ \hline \cdots \\ \hline 365. \text{ day}\\ \quad $1\cdot (1.01)^{364} + $1\cdot (1.01)^{364} * 1\ \% \\ \quad = $1\cdot (1.01)^{364} + $1\cdot (1.01)^{364}\cdot 0.01 = $1\cdot (1.01)^{364}\cdot (1+ 0.01) = $1\cdot (1.01)^{364}\cdot (1.01) = \mathbf{$1\cdot (1.01)^{365}} \\ \hline \end{array} }$

So we have:

$\begin{array}{|rcll|} \hline $1\cdot (1.01)^{365} = $1\cdot 37.7834343329 = $37.78 \\ \hline \end{array}$

If i have 1$ increasing 1% every day for one year, how do i calculate it in %? 100(1+0.01)^365??

FV = PV [1 + R]^N

FV = 1 [1 + 0.01]^365

FV = 1 x 1.01^365

FV = 1 x 37.78

FV = $37.78 - This is the value of $1 that increases by 1% each day for 365 days!.

If you want to know what is the percentage increase, then you have:

37.78/1 - 1 x 100 =3,678% percentage increase in the value of $1 in 1 year.