3. how much principal would you have to deposit to earn $1,000 simple interest in 7 1/2 years at a rate of…

Explanation:

Step1: Recall simple - interest formula

The simple - interest formula is $I = Prt$, where $I$ is the interest, $P$ is the principal, $r$ is the annual interest rate (in decimal form), and $t$ is the time in years. We need to solve for $P$, so we can rewrite the formula as $P=\frac{I}{rt}$.

Step2: Convert the rate and time to appropriate forms

The annual interest rate $r = 2.5%=0.025$, and the time $t = 7.5$ years, and the interest $I = 1000$.

Step3: Substitute values into the formula

$P=\frac{1000}{0.025\times7.5}$. First, calculate $0.025\times7.5 = 0.1875$. Then, $P=\frac{1000}{0.1875}=\frac{1000\times10000}{1875}=\frac{10000000}{1875}=\frac{10000000\div125}{1875\div125}=\frac{80000}{15}=\frac{16000}{3}\approx5333.33$.

Answer:

$$5333.33$