what is the effective interest rate of a simple discount note for $2700 at a bank discount rate of 12.25%, for 36 months?
To calculate the effective interest rate of a simple discount note, we need to use the formula:
Effective Interest Rate = (Discount / Face Value) x (365 / Number of Days)
First, let's calculate the discount:
Discount = Face Value x Bank Discount Rate x Time
Discount = $2700 x 0.1225 x (36/12)
Discount = $2700 x 0.1225 x 3
Discount = $989.25
Next, let's calculate the face value:
Face Value = Discount + Principal
Face Value = $989.25 + $2700
Face Value = $3689.25
Now, let's calculate the effective interest rate:
Effective Interest Rate = (Discount / Face Value) x (365 / Number of Days)
Effective Interest Rate = ($989.25 / $3689.25) x (365 / 36)
Effective Interest Rate = 0.2681 x 10.1389
Effective Interest Rate = 0.03123745
Therefore, the effective interest rate of the simple discount note is approximately 3.12%.
To find the effective interest rate of a simple discount note, you need to calculate the annual percentage rate (APR).
The formula to calculate the effective interest rate is:
Effective Interest Rate = ((Discount Rate / (1 - (Discount Rate x Time))) x 100)
In this case, the bank discount rate is 12.25% and the time is 36 months.
First, convert the bank discount rate to a decimal by dividing it by 100:
Discount Rate = 12.25% / 100 = 0.1225
Next, substitute the values into the formula:
Effective Interest Rate = ((0.1225 / (1 - (0.1225 x 36))) x 100)
Now, calculate the value inside the parentheses:
0.1225 x 36 = 4.41
1 - 4.41 = -3.41
Now, substitute the value back into the formula and calculate the effective interest rate:
Effective Interest Rate = ((0.1225 / -3.41) x 100)
0.1225 / -3.41 = -0.03594
-0.03594 x 100 = -3.594
The effective interest rate of the simple discount note is approximately -3.594%.
Note that if the result is negative, it means the effective interest rate is a discount, not an interest rate.