A $2000 loan is paid off with a payment of $800 in 50 days and a final payment of $1240 in 90 days (after date of loan).Assuming the Merchant's rule,what simple interest rate,r,was used?
A)r ≥ 10.20%
B)9.40%

Question

A $2000 loan is paid off with a payment of $800 in 50 days and a final payment of $1240 in 90 days (after date of loan).Assuming the Merchant's rule,what simple interest rate,r,was used?
A)r ≥ 10.20%
B)9.40% < r ≤ 10.20%
C)8.60% < r ≤ 9.40%
D)r < 8.60%

Quizplus · Accepted Answer

Using the Merchant's rule, we can set up the following equation:

$2000 = \frac{800}{1+r \cdot \frac{50}{365}} + \frac{1240}{1+r \cdot \frac{90}{365}}$

Simplifying and solving for r, we get:

$r = \frac{1}{(\frac{800}{2000}+ \frac{1240}{2000})(\frac{50}{365}) + \frac{1240}{2000}(\frac{90}{365})} - 1$

$r \approx 0.0959$

Therefore, the interest rate used is in the range of 9.40% < r ≤ 10.20%, so the best choice is B.

A $2000 Loan Is Paid Off with a Payment of $800