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.