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 Profit & Loss « PreviousNext » Algebra - II 
Author: S.LAL
Created: 18 Aug, 2010; Last Modified: 17 May, 2026

Commercial Mathematics - 03

Simple Interest

Interest is the money paid for the use of borrowed money (money taken as loan). The interest is paid by the money borrower to the money lender (such as a bank). Interest is always stated as a percentage of the loan, and is then known as the interest rate (R) while the loan value is called the principal (P). The sum of the principal and the interest is known as the amount (A). This is the total sum to be paid to the lender.

When interest is calculated only on the original principal, it is called simple interest (S.I.).

The interest rate R is generally expressed as a certain percentage of the principal P for one year, expressed as R% p.a. (per annum). The total interest is the annual interest multiplied by the number of years the loan (principal) continues to be with the borrower before he/she returns it to the lender.

Find the simple interest on `728 for 5 years at 4% per annum? (Chakravarti, Arithmetic, p. 315 Example 2)

Interest on `728 for one year = 4 %  of  728 = 728 × 4 100

∴ the interest for 5 years = 728 × 4 100 × 5 = 728 × 4 × 5 100 = 145.60

Hence, the accumulated interest for 5 years is `145.60.

The above example leads to the Simple Interest formula which connects the interest to the principal, the interest percentage and the interest term period.

S.I. = P × R × T 100

.......(1)

where:

S.I. = interest;     P = principal;
R = interest rate %;     T = time period

And, of course,

A = P + S.I.

.......(2)

where A = amount

In Eq. , the time period T may be in terms of months or years, although the latter is more common.

At what rate percent will `425 amount to `476 in 3 years? (Chakravarti, Arithmetic, p. 317 Example 1)

Given A = `476; P = `425; T = 3yrs

Let R be the rate percent. Therefore, using the Simple Interest formula:

S.I. = P × R × T 100 ⇒ 476 − 425 = 425 × R × 3 100 ⇒ ( 476 − 425 ) × 100 425 × 3 = R ⇒ R = 51 17 × 100 425 × 3 = 17 × 100 4 425 17 = 17 × 4 17 = 4

Thus, the interest rate percent is 4%.

Find the interest on `300 from March 5 to July 29 at per annum. (Bansal, Mathematics Class IX, p. 37, Ex. 1)

The number of days between March 5 and July 29
= 26 + 30 + 31 + 30 + 29 = 146   days

Therefore, the time period T = 146 365 yrs .

S.I. = P × R × T 100 = 300 × 15 × 146 100 × 4 × 365 = 4.50

Thus, the interest is `4.50.

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List of References

Bansal, RK, Concise Mathematics I.C.S.E., Part I – Class IX, New Delhi: Selina Publishers, 2005.
Chakravarti, JC, Arithmetic, 55th edn, Kolkata, India: MC Chakravarti, 1992.

Bibliography

Chakravarti, JC, Arithmetic, 55th edn, Kolkata, India: MC Chakravarti, 1992.
Thompson, JE, Arithmetic for the Practical Man, 3rd edn, NJ: Van Nostrand's Reinhold Company Inc., 1962.

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