On January 15, Mario signed a contract to pay Stephan $12,000 plus 9% 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 solve this problem, we need to first calculate the total amount Mario owes Stephan on both contracts:

Amount owed on May 15 = $12,000 + 9% of $12,000 = $13,080
Amount owed on September 12 = $18,000 + 10% of $18,000 = $19,800
Total amount owed = $13,080 + $19,800 = $32,880

On August 15, Stephan sells the contracts to Sally and Anna. To determine the amount Stephan received, we need to calculate the present value of the contracts at the rates Sally and Anna paid. We can use the formula:

Present value = Future value / (1 + r)^n

where r is the interest rate and n is the number of periods.

For the first contract, Sally paid 11%, so the present value is:

PV = $13,080 / (1 + 0.11)^0.67 ≈ $12,077.48

For the second contract, Anna paid 12%, so the present value is:

PV = $19,800 / (1 + 0.12)^1.93 ≈ $17,953.85

The total amount Stephan received on August 15 is the sum of the present values of the two contracts:

$12,077.48 + $17,953.85 ≈ $30,031.33

Therefore, the best choice is B: $31,030.33.

On January 15, Mario Signed a Contract to Pay Stephan