Note Present Value
1. **Problem Statement:** Wright Transport sold buses and received a note payable of 530000 due in 3 years with an 8% effective interest rate. We need to find the sales revenue recognized on January 1, 2024, which is the present value (PV) of the note.
2. **Formula and Explanation:** The present value of a single future amount is calculated using the formula:
$$PV = \frac{FV}{(1 + r)^n}$$
where $FV$ is the future value, $r$ is the interest rate, and $n$ is the number of periods.
3. **Calculation:** Here, $FV = 530000$, $r = 0.08$, and $n = 3$.
$$PV = \frac{530000}{(1 + 0.08)^3} = \frac{530000}{1.259712} \approx 420523.44$$
4. **Interpretation:** Wright Transport recognizes sales revenue of approximately 420523.44 on January 1, 2024.
5. **Journal Entries:**
- On January 1, 2024 (sale of merchandise):
- Debit Notes Receivable 420523.44
- Credit Sales Revenue 420523.44
- On December 31, 2024 (interest accrual):
- Interest = $420523.44 \times 0.08 = 33641.88$
- Debit Interest Receivable 33641.88
- Credit Interest Revenue 33641.88
- On December 31, 2025 (interest accrual):
- New principal = $420523.44 + 33641.88 = 454165.32$
- Interest = $454165.32 \times 0.08 = 36333.23$
- Debit Interest Receivable 36333.23
- Credit Interest Revenue 36333.23
- On December 31, 2026 (receipt of payment):
- Principal + interest accrued = $454165.32 + 36333.23 + (interest on 2026 principal)$
- Interest on 2026 principal = $(454165.32 + 36333.23) \times 0.08 = 39339.16$
- Total payment = $530000$
- Debit Cash 530000
- Credit Notes Receivable 420523.44
- Credit Interest Receivable (33641.88 + 36333.23) = 69975.11
- Credit Interest Revenue 39339.16
This completes the recognition and accounting for the note and interest.