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# True Discount Aptitude Question And Answer With Explanation

## Best explanation to understand and solve the true discount problems.

This section contains the aptitude questions based on TRUE DISCOUNT.

Here, you have the explanation for true discount, some important terms of true discount and also the important formulas of true discount.

Learn the given explanation and try to find the solution for the aptitude questions in our website which will be a practice for you to attend any entrance or competitive exams.

### What is meant by true discount?

True discount is the difference between the present worth of the money and the actual amount.

It can also be said as the interest in any present worth for the amount of time, the debt is due to be discharged.

What is the concept of true discount?

Consider a merchant ‘A’ buys goods worth of face value Rs. 2000 (including the interest for one year) from another merchant ‘B’ at a credit of say 12 months or one year. The ‘B’ prepares a bill called the bill of exchange, which is also known as Hundi. The merchant ‘A’ will sign this bill that allows ‘B’ to withdraw the amount from his bank account after the given period of 12 months.

What is nominal due date and legally due date?

Now, let the market interest rate is 5%. The exact date after the given period of 12 months is called the nominal due date. Also , 3 days grace period is also given to this date of expiry and this date is legally the due date.

For example: If 10th January  2010 is the nominally due date, 13 January 2010 will be legally due date.

The amount Rs. 2000 is called the face value. So, according to the bill, the ‘B’ will receive a face value of Rs. 2000 after twelve months.

But suddenly after 6 months, ‘B’ says that he needs money immediately and he cannot wait till due date. In this case, ‘B’ can approach a bank or broker to pay him money against this bill. In such a situation, the money given by the banker to ‘B’ will be less than the face value of the bill.

How is present value of bill calculated?

The present value of the bill is calculated by

PV  x (1+r x T) = FV

PV = present value

r = rate of interest

t = time

FV= face value

So, the present value or the true value is equal to 2000 / 1.025 which is equal to 1951.23

so, true discount = Face value - Present value that is 2000 - 1951.23 which is equal to  48.77

The true discount is nothing but the difference between the face value or sum due at the end of the given time and its present worth. So, in the given example,

True discount = Face value - Present value. That is 2000 - 1951.23 = 48.77

In other words, the true discount is the simple interest on the present value or worth for the unexpired time.

In other words, the present value or present worth of a sum of money due at the end of a specified time is that sum which will amount to the sum due with its interest for the given time at the given rate.

So, if the bank pays Rs. 1951.23 (present worth) to ‘B’ in exchange for the bill, the bank would not make a profit from this deal.

So, the bank will not use true discount but uses another method or formula to calculate the discount which is called Banker's Discount.

1.

Find the difference between the commercial and true discount on a bill of Rs 11524.80 due in 4 months at 6¼ per cent.

2.

If Rs 267 is the true discount on a certain sum of money due in eight months at 9% per annum, then what was the sum due ?

3.

Calculate the present worth of Rs 13860 due 2½ years ,the interest rate being 15% per annum.

4.

Mr Sippy forgot to pay the company bill for 1 year after getting notification he talk to the had and they agree to take immediate payment of the half amount of the bill and to postpone the payment of the other half of the bill for 2 years. In this process company gains Rs 40 . Calculate the amount of the bill if the money be worth 12½%.

5.

When true discount is subtracted from simple interest on a certain amount of money for 6 months at 12½% per annum we got a resultant of Rs 125.Calculate the amount of money.

6.

The interest on Rs 7500 which kept for 2 years is same as the true discount on Rs 9600 which is not paid for 2 years. If the rate of interest in both case is same, calculate the rate of interest.

7.

Sibsadhan purchased a Renault Kwid car for Rs 300000 and on the same day he give it for Rs 360000, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum then calculate he's gain.

8.

If the Moselle river is flowing at a rate of 4 km/hr , the area goes by the tank barge from one point to another point is 64 km and it return to the start point, it goes in upstream and return in downstream. Assume that the rate of tank barge in not moving water be 12 km/hr, then find the time taken by the tank barge in its whole journey.

9. Mr Gupta purchased a mobile for Rs. 6000 and sold it the same day for Rs. 7200, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then how much Mr Gupta gain :
10. What is the rate of interest if the true discount on Rs 350 unpaid for 2 years hence is Rs 100 ?
11. Find the rate % when the interest on the present value on Rs. 12630 which is unpaid for 8 months is Rs. 610.
12. A man purchased a cow for Rs. 2000 and sold it the same day for Rs. 2600, allowing the buyer a credit of 1 years. If the rate of interest be 5% per annum, then the man has a gain of:
13. A man purchased a cow for Rs. 4000 and sold it the same day for Rs. 4600, allowing the buyer a credit of 3 years. If the rate of interest be 15% per annum, then the man has a gain of:
14. A man purchased a cow for Rs. 3500 and sold it the same day for Rs. 3000, allowing the buyer a credit of 6 years. If the rate of interest be 10% per annum, then the man has a gain of:
15. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 45 and Rs. 40 respectively. The sum is:
16. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 55 and Rs. 50 respectively. The sum is:
17. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 65 and Rs. 60 respectively. The sum is:
18. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 75 and Rs. 70 respectively. The sum is:
19. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 95 and Rs. 90 respectively. The sum is:
20. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 105 and Rs. 100 respectively. The sum is:
21. The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 115 and Rs. 120 respectively. The sum is:
22. By investing in 15 (2/3)% stock at 50, one earns Rs. 1000. The investment made is:
23. By investing in 17( 2/3)% stock at 70, one earns Rs. 2000. The investment made is:
24. By investing in 18 (2/3)% stock at 80, one earns Rs. 2500. The investment made is:
25. By investing in 21(2/3)% stock at 110, one earns Rs. 4000. The investment made is:
26. By investing in 19(2/3)% stock at 90, one earns Rs. 3000. The investment made is:
27. By investing in 20(2/3)% stock at 100, one earns Rs. 3500. The investment made is: