Final answer:
To calculate the effective interest rate of the note, the present value is first calculated, then the interest, and finally, the effective rate is determined by annualizing the quarterly interest. However, the result does not match the multiple-choice options provided, suggesting the need for reevaluation based on specific terms of the note.
Step-by-step explanation:
To calculate the effective interest rate on a 3-month noninterest-bearing note with a maturity value of $205,000 and a stated annual interest rate of 12.4%, we first need to figure out the present value of the note. This is done by using the formula for present value, which in this case is the maturity value divided by the sum of 1 plus the interest rate (expressed as a decimal) raised to the power of the number of periods.
The formula looks like this: Present Value = Maturity Value / (1 + r)^n, where 'r' represents the interest rate per period and 'n' represents the number of periods until maturity. Since the note is for 3 months, we are dealing with one quarter of a year, so we use (12.4% / 4) for 'r' and 1 for 'n' as it is a single period (quarter). Using this approach, the calculation is as follows:
Present Value = $205,000 / (1 + 0.124/4)^1 = $205,000 / (1 + 0.031) = $205,000 / 1.031 = $198,837.43 approximately.
We then find the interest by subtracting the present value from the maturity value: $205,000 - $198,837.43 = $6,162.57. Finally, the effective interest rate (annualized) is calculated by dividing the interest by the present value and then multiplying by the number of periods in a year (4 for quarterly):
Effective Interest Rate = ($6,162.57 / $198,837.43) x 4 = 0.12395 x 4 = 0.4958 or 49.58%