trevor has an investment worth $6,774.50. he made his only deposit in it 22 years ago. given that the…

Explanation:

Step1: Recall simple - interest formula

The formula for simple interest is $A = P(1+rt)$, where $A$ is the final amount, $P$ is the principal (initial deposit), $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. Given $A=$6774.50$, $r = 0.027$ (since $2.7%=0.027$), and $t = 22$ years. We need to solve for $P$.

Step2: Rearrange the formula for $P$

Starting from $A = P(1 + rt)$, we can solve for $P$ by dividing both sides of the equation by $(1+rt)$. So $P=\frac{A}{1+rt}$.

Step3: Substitute the values

Substitute $A = 6774.50$, $r=0.027$, and $t = 22$ into the formula: [ \begin{align*} P&=\frac{6774.50}{1+(0.027\times22)}\ &=\frac{6774.50}{1 + 0.594}\ &=\frac{6774.50}{1.594}\ &= 4250 \end{align*} ]

Answer:

C. $$4,250.00$