How to Calculate the Rate of Interest on a Discounted Bill of Exchange

In this post, we will solve the question:

A bill of ₹10,100 drawn on 14th January for 5 months was discounted on 26th March. The customer was paid ₹9,939.25. Calculate the rate of interest.

Understanding the Problem

A bill of exchange is a written order used in trade that binds one party to pay a fixed sum to another party on demand or at a predetermined date.

Discounting a bill means selling it to a bank before maturity to receive funds immediately. The bank deducts a certain amount called the discount, which acts as interest for the remaining time until maturity.

Step-by-Step Solution

Step 1: Find the maturity date

• Drawn on: 14th January
• Term: 5 months → Maturity date = 14th June
• Add 3 days grace: 14th June + 3 days = 17th June

Step 2: Calculate the discount period

• From 26th March to 31st March = 5 days
• April = 30 days
• May = 31 days
• June until 17th = 17 days
• Total = 83 days

Step 3: Find the discount amount

Bill amount = ₹10,100

Amount received = ₹9,939.25

Discount = 10,100 − 9,939.25 = ₹160.75

Step 4: Calculate the rate of interest

Formula:

Rate of Interest = (Discount / Bill Amount) × (365 / Discount Period) × 100

Substitute values:

= (160.75 / 10100) × (365 / 83) × 100
= 0.01591584 × 4.39759036 × 100
≈ 7% per annum
    

Final Answer

The rate of interest is approximately 7% per annum.

Key Points to Remember

• Always add the 3 days grace period when calculating maturity dates for bills of exchange.
• The discount period is from the date of discounting to the maturity date.
• Check all calculations to avoid mistakes.