a simple discount note for $6,600 at a ordinary bank discount rate of 8.61% for 60 days. What is the effective interest rate? Round to the nearest tenth of a percent
Vvbg
To calculate the effective interest rate for a simple discount note, we can use the following formula:
Effective Interest Rate = (Discount / Face Value) * (360 / Days)
First, let's calculate the discount amount:
Discount = Face Value * Bank Discount Rate * (Days / 360)
Given information:
Face Value = $6,600
Bank Discount Rate = 8.61%
Days = 60
Calculating the discount amount:
Discount = $6,600 * 8.61% * (60 / 360) = $86.10
Now, let's calculate the effective interest rate:
Effective Interest Rate = ($86.10 / $6,600) * (360 / 60)
Effective Interest Rate = 0.0131 * 6
Effective Interest Rate = 0.0786
Converting it to a percentage, rounded to the nearest tenth:
Effective Interest Rate = 7.9%
To find the effective interest rate, we need to use the formula:
Effective Interest Rate = (Discount/Principal) * (360/Number of Days)
Given:
Discount (D) = $6,600
Ordinary Bank Discount Rate (R) = 8.61% = 0.0861
Number of Days (N) = 60
First, let's find the Principal (P):
Principal (P) = Discount / (1 - Rate * Time)
P = D / (1 - R * N/360)
P = 6600 / (1 - 0.0861 * 60/360)
P = 6600 / (1 - 0.861/6)
P = 6600 / (1 - 0.1435)
P = 6600 / 0.8565
P ≈ $7697.29
Now, substitute the values in the formula to find the effective interest rate (EIR):
EIR = (D / P) * (360 / N)
EIR = (6600 / 7697.29) * (360 / 60)
EIR ≈ 0.857 * 6
EIR ≈ 5.142
Round the effective interest rate to the nearest tenth of a percent:
EIR ≈ 5.1%
Therefore, the effective interest rate is approximately 5.1%.