Question

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should have a comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round to two decimal places, show both decimal places (5.06). how long does it take $450 to double at a simple interest rate of 100%? express your answer in years.

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $A = P(1+rt)$, where $A$ is the final amount, $P$ is the principal amount, $r$ is the annual interest rate, and $t$ is the time in years. We want to double the principal, so $A = 2P$, and $r = 1$ (since $100\%=1$).

Step2: Substitute values into the formula

Substitute $A = 2P$ and $r = 1$ into $A = P(1+rt)$:
\[

$$\begin{align*} 2P&=P(1 + 1\times t)\\ 2P&=P(1 + t) \end{align*}$$

\]
Since $P
eq0$ (because we have a non - zero principal of $\$450$), we can divide both sides of the equation by $P$:
\[

$$\begin{align*} \frac{2P}{P}&=\frac{P(1 + t)}{P}\\ 2&=1 + t \end{align*}$$

\]

Step3: Solve for $t$

Subtract 1 from both sides of the equation $2=1 + t$:
\[t=2 - 1=1\]

Answer:

$1$