Using the Merchant's rule,a debt of $4000 is paid off as follows: $1000 in 30 days from today,$2000 in 60 days from today,and a final payment of $1026.51 in 80 days from today.What simple interest rate,r,was used?
A)r

Question

Using the Merchant's rule,a debt of $4000 is paid off as follows: $1000 in 30 days from today,$2000 in 60 days from today,and a final payment of $1026.51 in 80 days from today.What simple interest rate,r,was used?
A)r < 4%
B)4% < r < 4.5%
C)4.5% < r < 5.0%
D)5.0% < r

Quizplus · Accepted Answer

The Merchant's rule is used to calculate the interest rate in a situation where a debt is paid off in parts at different times. The formula for the Merchant's rule is: $ r = \frac{I}{P \times t} $, where $I$ is the interest, $P$ is the principal, and $t$ is the time in years. In this case, the total payments made are $1000 + $2000 + $1026.51 = $4026.51, meaning the interest paid is $4026.51 - $4000 = $26.51. The average time for the payment can be calculated as a weighted average of the payments: $ \frac{(1000 \times 30) + (2000 \times 60) + (1026.51 \times 80)}{4026.51} \approx 59.96 $ days, or approximately $ \frac{59.96}{365} \approx 0.164 $ years. Using the Merchant's rule formula, $ r = \frac{26.51}{4000 \times 0.164} \approx 0.0403 $ or 4.03%, which falls into the range of 4% < r < 4.5%.

Using the Merchant's Rule,a Debt of $4000 Is Paid Off