A man has a simple discount note for $6 comma 500, at an ordinary bank discount rate of 8.61 % comma for 50 days. What is the effective interest rate? Round to the nearest tenth of a percent
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 need to first calculate the discount amount and then use it to find the effective interest rate.
Step 1: Calculate the Discount Amount
The discount amount on a simple discount note can be found using the formula:
Discount Amount = Principal × Interest Rate × Time
Given:
Principal (P) = $6,500
Interest Rate (R) = 8.61% (expressed as a decimal by dividing by 100) = 0.0861
Time (T) = 50 days
Discount Amount = $6,500 × 0.0861 × 50
Step 2: Calculate the Effective Interest Rate
The effective interest rate can be found using the formula:
Effective Interest Rate = (Discount Amount / Principal) × (365 / Time)
Effective Interest Rate = (Discount Amount / Principal) × (365 / Time)
Note: 365 is used since the time is given in days.
Effective Interest Rate = (Discount Amount / $6,500) × (365 / 50)
Now, let's calculate the Discount Amount:
Discount Amount = $6,500 × 0.0861 × 50
= $2,791.25
Substituting the values:
Effective Interest Rate = ($2,791.25 / $6,500) × (365 / 50)
Calculating:
Effective Interest Rate ≈ 0.4291 × 7.3
Effective Interest Rate ≈ 3.1287
Rounding to the nearest tenth of a percent:
Effective Interest Rate ≈ 3.1%
Therefore, the effective interest rate is approximately 3.1%.