Question

grab bag
a $10,000 t - bill maturing in 83 days was sold for $10,087.22. find the simple discount and equivalent simple interest rates.
10numeric 1 point
what is the simple interest rate (round to two decimals)?
answer

Explanation:

Step1: Calculate discount amount

$D = 10000 - 10087.22 = -87.22$
(Note: Negative discount means premium, adjust for interest)

Step2: Define time in years

$t = \frac{83}{365}$

Step3: Use simple interest formula

$I = P \times r \times t$, rearrange to $r = \frac{I}{P \times t}$
Here, $I = 87.22$, $P = 10087.22$
$r = \frac{87.22}{10087.22 \times \frac{83}{365}}$

Step4: Compute denominator first

$10087.22 \times \frac{83}{365} \approx 10087.22 \times 0.227397 \approx 2293.93$

Step5: Calculate interest rate

$r \approx \frac{87.22}{2293.93} \approx 0.0380$

Answer:

3.80%