A man has a simple discount note for $6,500 at an ordinary bank discount rate of 8.61 %, for 50 days. What is the effective interest rate? Round to the nearest tenth of a percent
To find the effective interest rate, we can use the formula:
Effective Interest Rate = (Discount / Face Value) * (360 / T)
Where:
Discount = Face Value - Amount Received
Face Value = $6,500 (given)
T = Number of days until maturity (50 days in this case)
360 = Number of days in a year for bank interest calculations
First, we need to calculate the discount:
Discount = Face Value * Bank Discount Rate
Discount = $6,500 * 0.0861
Discount = $560.65
Next, we calculate the amount received:
Amount Received = Face Value - Discount
Amount Received = $6,500 - $560.65
Amount Received = $5,939.35
Now, we can calculate the effective interest rate:
Effective Interest Rate = (Discount / Face Value) * (360 / T)
Effective Interest Rate = ($560.65 / $5,939.35) * (360 / 50)
Effective Interest Rate ≈ 0.0944 * 7.2
Effective Interest Rate ≈ 0.6816
Rounding to the nearest tenth of a percent, the effective interest rate is approximately 0.7%.