Simple Interest and Compound Interest (SI and CI)- Important Formulae, Tricks and Shortcuts [Quantitative Aptitude]

Here are important formulas and shortcuts to solve problems related to Simple Interest and Compound Interest. Basic knowledge regarding calculating SI and CI is important for various competitive exams like IBPS, SBI Bank PO, assistant, SSC exams, Railway exam, UPSC exams.

What is Simple Interest?

Suppose Ramesh borrowed 1000 rupees from Bank. This is called Principle (P) amount.
Now while lending money Bank asked him to pay extra 5% or Rs 50/1000. Here 5% is called Rate of Interest (R).
Ramesh has promised to pay the money back after two years with interest, so 2 years is Time period (T).
As Ramesh has to pay Rs. 50/1000 per year, so after two years he has to pay Rs. 100 extra. This extra money is called Simple Interest (SI).
After two years Ramesh will pay (1000+100) = Rs. 1100 to Bank. Money paid back is called Amount.

Important Formulae on Simple Interest:

SI = (P * R * T) / 100

P = (SI * 100) / (R * T)

R = (SI * 100) / (P * T)

T = (SI * 100) / (P * R)

Amount = Principle + SI.

What is Compound Interest?

Taking same case we discussed above Ramesh borrowed Rs. 1000 from a Bank at 5% Rate of Interest for Time Period of 2 years, but bank has asked him to pay compound interest annually. So in this case amount will be calculated annually.

After one year amount will be P + SI = 1000 + 50 = 1050.
So for second year Principle will be 1050.
SI for second year = (1050 * 5 * 1) / 100 = 52.50
So amount after 2nd year will be P + SI = 1050 + 52.50 = 1102.50.
Hence Compound Interest (CI) he paid = 1102.50 - 1000 = 102.50.

Important Formulae on Compound Interest:

I. When CI is calculated Annually:

Amount = P * (1+R/100)^T

CI = Amount - Principle

II. When CI is calculated Half - yearly:

Amount = P * {1+(R/2)/100}^2T

CI = Amount - Principle

III. When CI is calculated Yearly but time is given in fraction say 2 (1/2) years ( 2 and half year).

Amount = P * (1+R/100)² * {1 + ((1/2) * R)/100}

IV. When Rates of Interest are different for different years, say R1,%, R2%, R3% for 1st, 2nd and 3rd year.

Amount = P * (1 + R1/100) * (1 + R2/100) * (1 + R3/100).

V. Concept of Equal Installment when interest is compounded annually:

Let us suppose P money is borrowed for 2 years at R rate of interest and we have to return the money in 2 equal installments annually. Then the installments will be?

If installment = X

P = X / (1 + R/100) + X / (1+R/100)²

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