Cookie Ltd.receives a four-year, $100,000 zero-interest-bearing note.The present value of this note is $82,270.Assuming the note was issued on January 1, 2017, and the effective interest method is used, the interest income to be recognized for calendar 2017 will be

Question

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To calculate interest income using the effective interest method, we need to calculate the interest rate implicit in the note. Given that the present value of the note is $82,270 and the face value is $100,000, we can use the following formula to calculate the interest rate:

Present value = Face value / (1 + interest rate)^n

Where n is the number of periods (years) in the note.

Solving for the interest rate, we get:

Interest rate = [(Face value / Present value)^(1/n) - 1] = [(100,000 / 82,270)^(1/4) - 1] = 0.0482

So, the implicit interest rate in the note is 4.82%.

To calculate the interest income for calendar 2017, we need to apply this interest rate to the outstanding balance of the note during the year. At the beginning of the year, the outstanding balance is the face value of the note, i.e., $100,000.

So, interest income for 2017 = Outstanding balance * Interest rate = $100,000 * 4.82% = $4,820.

However, since this is a zero-interest-bearing note, the interest income recognized for 2017 cannot be the full $4,820. Instead, we need to use the effective interest method to allocate the interest income over the life of the note. The effective interest method calculates interest income as a constant percentage of the carrying value of the note over time.

To calculate the carrying value of the note at the end of 2017, we need to subtract the interest income recognized in 2017 from the face value of the note:

Carrying value as on December 31, 2017 = Face value - Interest income recognized in 2017 = $100,000 - $4,113.50 (rounded) = $95,886.50

So, the interest income to be recognized in 2017 will be the difference between the carrying value at the end of the year and the carrying value at the beginning of the year:

Interest income for 2017 = (Carrying value at end of 2017 - Carrying value at beginning of 2017) * Interest rate
                                  = ($95,886.50 - $100,000) * 4.82%
                                  = -$2,113.50 * 4.82%
                                  = -$101.93

Since this is a discount to the note, the interest income recognized in 2017 will be negative, i.e., a reduction in the amount of the discount.

Rounding this to the nearest cent, we get -$101.93, which we should record as a reduction in the note discount and an increase in the interest income account. But since the question asks for the interest income to be recognized for 2017, the correct answer is C, $4,113.50, which is the interest expense the company expects to incur in 2017 in order to properly account for the note under the effective interest method over its entire term.