On January 15, Mario signed a contract to pay Stephan $12,000 plus 9% simple interest on May 15 and $18,000 plus 10% interest on September 12. On August 15, Stephan then sold the first contract to Sally at a rate of 11% and the other contract to Anna for 12%. Determine the amount Stephan received on August 15.
A) $33,333.33
B) $31,030.33
C) $30,130.33
D) $29,313.33
E) $26,613.33

Question

Quizplus · Accepted Answer

To determine the amount Stephan received on August 15, we need to calculate the value of each contract at the time of sale, considering the interest rates and the time periods involved.1. For the first contract ($12,000 plus 9% simple interest due on May 15):- The interest period from January 15 to May 15 is 4 months.- The interest amount is $12,000 \times 0.09 \times \frac{4}{12} = 360$.- The total amount due on May 15 is $12,000 + 360 = 12,360$.- Stephan sells this contract to Sally on August 15, which is 3 months after May 15.- The interest Sally agrees to pay is 11% for 3 months: $12,360 \times 0.11 \times \frac{3}{12} = 339.90$.- The total amount Stephan receives for this contract is $12,360 + 339.90 = 12,699.90$.2. For the second contract ($18,000 plus 10% interest due on September 12):- The interest period from January 15 to September 12 is approximately 8 months.- The interest amount is $18,000 \times 0.10 \times \frac{8}{12} = 1,200$.- The total amount due on September 12 is $18,000 + 1,200 = 19,200$.- Stephan sells this contract to Anna on August 15, which is 1 month before it's due.- The interest Anna agrees to pay is 12% for 1 month: $19,200 \times 0.12 \times \frac{1}{12} = 192$.- The total amount Stephan receives for this contract is $19,200 + 192 = 19,392$.Adding the amounts Stephan received for both contracts: $12,699.90 + 19,392 = 32,091.90$.Since the correct total amount is not listed in the options provided, it appears there may have been a mistake in the calculation or interpretation of the options. Based on the calculations provided, none of the options accurately reflect the correct total. However, the closest match to the process described would be option B) $31,030.33, assuming a recalibration of the calculation process or a misinterpretation of the interest calculations or sale conditions.

On January 15, Mario Signed a Contract to Pay Stephan