The present worth of the money is important to understand before dwelling into the true discount. Any money that is to be paid before the due date is cleared off for debt is known as the present worth of the money.

True discount can be understood in reference to this present worth. The difference between the present worth of the money and the amount is known as the true discount.

Also, it can be stated as the interest in any present worth for the amount of time the debt is due to be discharged.

**True Discount and Bankers Discount Formula**

There is always a big confusion between these two concepts. To understand both the concepts we will use an example.

Let us suppose that P has borrowed Rs. 1000 from Q. This amount taken by P has to be returned with interest after a period of 1 year. The market interest to be paid here is 5%.

For the payment, P gives Q a note having a face value of Rs. 1050. After 6 months Q demands the money to be paid immediately by P. He cannot wait for 6 more months for the repayment.

Thus, Q goes to the bank and gives the note with the face value of Rs. 1050 back to P. So, the present value of this Rs. 1050 note is calculated as,

PV x (1 + rt) = FV. Here, r is the simple interest, FV is the face value, and t is time. So, true value or present value here will be, 1050/1.025 = 1024.4.

Thus, true discount, in this case, is the difference between face value and true value. That is 1050 – 1024.4 = Rs. 25.6.

But the bank does not pay the 1024.4 to B. The bank uses another formula called banker’s discount rather than the true discount. So, in this case, Banker’s discount = FV x r x t = 1050 x 0.05 x 1/2 = Rs. 26.25.

Thus, this example clearly explains the difference between Banker’s discount and the true discount.

**Browse more Topics under Profit And Loss**

- Cost Price
- Fixed, Variable and Semi-variable Cost
- Selling Price
- Marked Price
- List Price
- Margin
- Dishonest Dealers and Faulty Weights
- Percentage Loss
- Percentage Gain
- Discounts and Marked Price
- Equivalent Discount
- Equation-Based Questions
- Goods Passing Through Successive Hands
- Bankers Discount
- Profit and Loss Practice Questions

*Learn more about Equivalent Discount here in detail*

**Examples on True Discount**

**Q. Suppose on Rs. 260 currently, the true discount is Rs. 20 after some time. Find out what will be the true discount on the same amount of money due after the passage of a quarter of the time. The rate of interest, in this case, remains the same.**

The formula to calculate the true discount directly is,

True discount = Rate x amount x time/(100 + (time x rate)

Thus, it becomes 20 = rate x time x 260/100 + (rate x time)

=> RT = 100/12.

So, required sum true discount = 260 x R x T/4/100+ RT/4 = 260 x 100/12/(400 + 100/12)

=> 269/49 = Rs. 5.3

**Practice Questions on True Discount**

Here **True discount=TD,Â Bankers discount=BD**

**Q. The TD of Rs. 1624 is the same as the BD of Rs. 1600 at the same time period and for the same rate of 6%. Find out the time interval between the legally due date and the date of discounting.**

A. 2 monthsÂ Â Â Â Â Â Â Â B. 3 monthsÂ Â Â Â Â Â Â Â Â Â Â C. 4 monthsÂ Â Â Â Â Â Â Â Â Â D. 6 months

**Answer:Â **B. 3 months

**Q. For 1 year on a certain sum, Banker’s gain is 1/10 of the TD. What will be the rate of percent per annum?**

A. 9 1/11 %Â Â Â Â Â Â Â Â Â B. 10 %Â Â Â Â Â Â Â Â Â Â Â Â Â Â C. 11 1/11%Â Â Â Â Â Â Â Â Â Â Â Â Â D. None of the above

**Answer:**Â B. 10 %

**Q. On Rs. 260, Rs. 20 is the TD after a certain time period. Find out what will be the TD on the same sum which will be due after 1/2 of the former time. Here, the rate of interest remains the same.**

A. Rs. 10Â Â Â Â Â Â Â Â Â Â Â B. Rs. 10.40Â Â Â Â Â Â Â Â Â C. Rs. 11.20Â Â Â Â Â Â Â Â Â Â Â D. Rs. 12

**Answer:**Â B. Rs. 10.40

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