True discount formula-Explained with Simple Examples

Last updated on July 3rd, 2025 at 11:44 am

So, many a times we are faced with a situation wherein due to the mathematical complexities the true value received or given is not clear. One such regular complexity of finance in daily life is experienced in the concept of “True Discount”. In this article , I will explain not only true discount but also true discount formula.

What is True Discount Formula?

The true discount formula any calculation is as follows;

 P= G X (1+Q/100) N-G

Where,

• P denotes the true discount,
• G Represents the present value of that item or sum
• Q represents rate of interest( simple interest)

The above true discount formula has been derived from the relation of simple interest and true discount, which is;

 P= (G x N x Q)/100

Where, N is nothing but the duration.

True Discount Example

So, let me explain the application of true discount formula with a very easy example.

Lets suppose A borrowed 1000 from B & Agreed to pay 5% Interest in one year.  Hence, the true discount in this case would be;

1000 x 1 x 5 /100= 50. Hence the true discount is nothing but 5% of the amount of money lent to B. But its application can be better understood on why this calculation is actually done. So lets assume that B goes to a bank after 6 months and says that I am in need of some funds and A owes me 1050. So the banker calculates the true discount for 6 months which is

1000 x 5 x 0.5/ 100=25.

So the banker gives B 1025 and will collect 1050 from A after 6 months making a gain of 2.5% interest.

True Discount Questions for Practice

Question 1: True Discount Questions

A bill of $1,500 is due in 3 months, and the true discount is $30. Calculate the rate of interest per annum.

a) 1%

b) 2%

c) 3%

Answer 1: The formula for true discount is: True Discount=Principal×Rate×Time100+Rate×TimeTrue Discount=100+Rate×TimePrincipal×Rate×Time​

Given, True Discount = $30, Principal = $1,500, and Time = 3 months.

Let the rate of interest be RR.

30=1500×R×312100+R×31230=100+R×123​1500×R×123​​

Solving this equation, we find R≈2%R≈2%.

So, the correct answer is b) 2%.

Question 2: True Discount Questions

If the true discount on a sum of money is $40, the rate of interest is 5% per annum, and the time is 6 months, find the principal amount.

a) $800

b) $1,000

c) $1,200

Answer 2: Principal=True Discount×100Rate×TimePrincipal=Rate×TimeTrue Discount×100​

Given, True Discount = $40, Rate = 5%, and Time = 6 months.

So, the correct answer is a) $800.

Question 3: True Discount Qustion

Find the true discount on a bill of $2,000 due in 9 months at an annual rate of 8%.

a) $120

b) $144

c) $160

Answer 3: True Discount=Principal×Rate×Time100+Rate×TimeTrue Discount=100+Rate×TimePrincipal×Rate×Time​

Given, Principal = $2,000, Rate = 8%, and Time = 9 months.

True Discount=2000×8×912100+8×912True Discount=100+8×129​2000×8×129​​

Solving this, we find True Discount ≈ $144.

So, the correct answer is b) $144.

Question 4: True Discount Question

A bill of $600 is discounted for 4 months, and the true discount is $24. Find the rate of interest per annum.

a) 4%

b) 6%

 c) 8%

Answer 4: Rate=True Discount×100Principal×TimeRate=Principal×TimeTrue Discount×100​

Given, True Discount = $24, Principal = $600, and Time = 4 months.

Rate=24×100600×412=24×100200=12%Rate=600×124​24×100​=20024×100​=12%

So, the correct answer is c) 8%

Question 5: True Discount Qustion

If the true discount on a bill is $90, the rate of interest is 6% per annum, and the time is 1 year, find the principal amount.

 a) $1,500

b) $1,800

c) $2,000

Answer 5: Principal=True Discount×100RatePrincipal=RateTrue Discount×100​

Given, True Discount = $90, Rate = 6%, and Time = 1 year.

.

So, the correct answer is a) $1,500.

Banker’s Discount vs True Discount

Both represent types of deduction applied to a future payable amount but they are based on totally different financial principles. These formula are needed for commercial transaction and interest based problems in competitive exams. True discount reflects the actual saving. It is the difference between the future value and present worth.

Banker’s Discount calculated remaining time maturity of the face value of a bill. It is the simple interest of the bill (face value). Making is alittle higher than the true discount. Banker’s discount overestimates cost of borrowing, this small difference is a big deal in banking and discounting scenarios.

Both involve calculating interest over time. True discount is more accurate in economic cost and banker’s discount is little inflated. For finance students this is used for discounting, loan repayment also time value money.

Present worth and True discount

They are closely related they are used to determine the actual value of future payments. Present worth as it says determines current value of a sum of payable in future date discounted at given rate.

True discount is difference between the future value and present worth which represents the interest saved when payment done before due date.

These are important concepts for finance students and professionals for job roles and exams. Understanding the relationship between present worth and true discount helps students master the time value of money.

FV = Face Value / Amount due

R = Interest Rate (% per annum)

T = Time (in years)

FAQ

Concept of True Discount used in real life?

True Discount is used in bill discounting, invoice financing, and understanding short-term loans. It’s a simplified form of discounting used by banks and financial institutions.

True Discount asked in competitive exams?

Yes. True Discount questions frequently appear in exams like SSC, Railways, Bank PO/Clerk, and MBA entrance tests. It’s part of the quantitative aptitude section.

What is true discount and simple interest formula?

TD = (P × R × T) / 100
where P is the Present Worth, R is the Rate of Interest per annum, and T is the Time (in years) until payment is due.

Simple interest:

SI=100 P×R×T​

• SI = Simple Interest
• P = Principal amount (initial sum)
• R = Rate of interest per annum (in %)
• T = Time (in years)

Did you know?
The concept of True Discount forms the mathematical basis for finance concepts like bond pricing, loan discounting, and time value of money. If you’re preparing for a finance career, mastering these basics is essential.
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