29. A company recognizes a $50,000, four-year, 4% note when the effective rate of interest was 5%. The following should be noted: Assume an annual interest rate of 5% for four years is appropriate, the present value of the principal is $50,000 X 0.8227 = $41,135, and the present value of the interest is $50,000 X 0.04 X 3.5459 = $7,090. Assume an annual interest rate of 4% for four years is appropriate, the present value of the note is $50,000 X 0.8548 = $42,740, and the present value of the interest is $50,000 X 0.04 X 3.6299 = $7,260. What is the amount of the discount, if any, on the notes receivable at the date of issuance?
Answer: B
The amount of the discount on the notes receivable at the date of issuance is $1,773.
To determine the discount on the notes receivable, we need to compare the present value of the note calculated using the effective interest rate of 5% with the amount recognized at issuance. The present value at the effective rate is $41,135, while the amount recognized is $42,740 based on the nominal rate of 4%. The discount is $42,740 - $41,135 = $1,605.
A) $7,560
This option is incorrect because it suggests a discount significantly higher than the calculated difference between the present value of the note at the effective rate and the issuance amount. The calculations show the discount is much lower than this figure.
B) $1,773
This option is correct as it accurately represents the discount on the notes receivable. The present value of the note at the effective interest rate of 5% is $41,135, and the recognized amount is $42,740, resulting in a discount of $1,773.
C) $7,092
This option is incorrect because it does not correlate with the calculated discount between the present values. The calculations do not support this amount as a valid discount, as it exceeds the calculated difference.
D) $2,000
This option is also incorrect as it overestimates the discount. The actual discount calculated from the present values does not approach this figure, making it an unreliable choice.
Conclusion
The correct answer is $1,773, as it reflects the accurate difference between the recognized amount of the notes receivable and the present value calculated at the effective interest rate. All other options either overstate the discount or fail to align with the calculations derived from the provided data.