Answer: $2,145,637.43.
Step-by-step explanation: To find the cash recorded on the issue date of the note, we need to consider the face value of the note and the market rate of interest.
Given:
- Face value of the note: $1,210,000
- Annual interest rate on the note: 8%
- Market rate of interest for a note of similar risk: 9%
1. Cash recorded on the issue date of the note:
The cash recorded on the issue date of the note is equal to the face value of the note. Therefore, the cash recorded on the issue date is $1,210,000.
2. Total proceeds:
The total proceeds include both the cash recorded and the interest expense that will accrue over the life of the note. To calculate the total proceeds, we need to find the present value of the note based on the market rate of interest.
Using the present value formula:
Present Value = Face Value / (1 + Market Rate)^Number of Periods
In this case:
Face Value = $1,210,000
Market Rate = 9%
Number of Periods = 3 years
Plugging in the values:
Present Value = $1,210,000 / (1 + 0.09)^3
Calculating further:
Present Value = $1,210,000 / (1.09)^3
Present Value ≈ $1,210,000 / 1.29503
Present Value ≈ $935,637.43
Therefore, the total proceeds would be the sum of the cash recorded and the present value:
Total Proceeds = Cash Recorded + Present Value
Total Proceeds ≈ $1,210,000 + $935,637.43
Calculating further:
Total Proceeds ≈ $2,145,637.43
Hence, the cash recorded on the issue date of the note is $1,210,000, and the total proceeds amount to approximately $2,145,637.43.