drill problem 10-11 (algo) lu 10-2 (1) required: solve for the missing item in the following. note: do not…

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the simple interest, $P$ is the principal, $r$ is the interest rate (in decimal form), and $t$ is the time in years. We are given $I=$160$, $r = 4.75%=0.0475$, and $t = 2.5$ years. We need to solve for $P$.

Step2: Rearrange the formula to solve for $P$

From $I = Prt$, we can isolate $P$ by dividing both sides of the equation by $rt$. So, $P=\frac{I}{rt}$.

Step3: Substitute the given values into the formula

Substitute $I = 160$, $r=0.0475$, and $t = 2.5$ into the formula $P=\frac{I}{rt}$. $P=\frac{160}{0.0475\times2.5}$ First, calculate $0.0475\times2.5=0.11875$. Then, $P=\frac{160}{0.11875}\approx1347.37$.

Answer:

$$1347.37$