Question

discounts versus simple discount rates
an insurance agent has just sold a large policy and will be paid a commission of $3,279.46 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.
9 numeric 1 point
what is the actual simple discount rate hed be paying?
answer

Explanation:

Step1: Calculate discount amount

The discount is 4% of the future commission.
$\text{Discount} = 0.04 \times 3279.46 = 131.18$

Step2: Find present value (cash received)

Subtract discount from future value.
$\text{Present Value} = 3279.46 - 131.18 = 3148.28$

Step3: Calculate time in years

30 days is $\frac{30}{365}$ of a year.
$t = \frac{30}{365} \approx 0.08219$

Step4: Use simple discount formula to find rate

Simple discount formula: $\text{Discount} = \text{Future Value} \times r \times t$, solve for $r$.
$r = \frac{\text{Discount}}{\text{Future Value} \times t} = \frac{131.18}{3279.46 \times 0.08219}$
$r \approx \frac{131.18}{269.54} \approx 0.4867$
Convert to percentage: $r \approx 48.7\%$

Answer:

$\boldsymbol{48.7\%}$ (rounded to one decimal place; or 48.67% for more precision)