Question

discount versus simple discount rate
an insurance agent has just sold a large policy and will be paid a commission of $3,294.45 in thirty days. his brother - in - law offers to give him cash right now in exchange for the check when it arrives, at a 4% discount. thinking that 4% sounds like a pretty sweet rate for a loan, the agent agrees.
10 numeric: 1 point
what is the equivalent simple interest rate?
answer

Explanation:

Step1: Calculate discount amount

Discount $D = F \times d \times t$
Where face value $F = \$3,219.45$, discount rate $d = 0.04$, time $t = \frac{30}{360}$ (using banker's rule for simple discount)
$D = 3219.45 \times 0.04 \times \frac{30}{360} = 3219.45 \times 0.04 \times \frac{1}{12} \approx 10.73$

Step2: Find proceeds (amount received)

Proceeds $P = F - D$
$P = 3219.45 - 10.73 = 3208.72$

Step3: Relate to simple interest formula

Simple interest $I = P \times r \times t$, and $I = D$ here
Rearrange to solve for $r$: $r = \frac{I}{P \times t}$

Step4: Compute equivalent interest rate

$r = \frac{10.73}{3208.72 \times \frac{30}{360}} = \frac{10.73}{3208.72 \times \frac{1}{12}} = \frac{10.73 \times 12}{3208.72} \approx \frac{128.76}{3208.72} \approx 0.0401$

Answer:

$\approx 4.01\%$