natalie needs a $5,800 loan to pay for living expenses during her first year of college. which loan option…

Explanation:

Step1: Identify the simple interest formula

The formula for simple interest is $I = P \times r \times t$, where $P$ is the principal, $r$ is the annual interest rate, and $t$ is the time in years.

Step2: Calculate interest for option F

$P = $5,800$, $r = 3.90% = 0.039$, $t = \frac{12}{12} = 1$ year. $$I_F = 5800 \times 0.039 \times 1 = $226.20$$

Step3: Calculate interest for option G

$P = $5,800$, $r = 2.25% = 0.0225$, $t = \frac{24}{12} = 2$ years. $$I_G = 5800 \times 0.0225 \times 2 = $261.00$$

Step4: Calculate interest for option H

$P = $5,800$, $r = 2.80% = 0.028$, $t = \frac{18}{12} = 1.5$ years. $$I_H = 5800 \times 0.028 \times 1.5 = $243.60$$

Step5: Calculate interest for option J

$P = $5,800$, $r = 3.40% = 0.034$, $t = \frac{36}{12} = 3$ years. $$I_J = 5800 \times 0.034 \times 3 = $591.60$$

Step6: Compare the interest amounts

Comparing $$226.20$, $$261.00$, $$243.60$, and $$591.60$, the smallest value is $$226.20$.

Answer:

F. A 12-month loan with a 3.90% annual simple interest rate.