# Compound and Simple interest in entrance exams

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1834 Compound and Simple interest question are applicable to all types of entrance exams like CAT, GMAT, SBI PO or any other Bank exam. Practicing these will develop your understanding on how to solve critical questions of Compound and simple interest question in entrance exams in lesser time, which can be a big factor in cracking any exam.

Lead-in to Simple and compound Interest:

Repo and reverse repo set by the Reserve Bank of India play a role in the interest you pay on a loan taken from the bank. Those having taken a loan do keep themselves acquainted with the monetary policy and interest rates. Simple interest & compound interest problems are generally about interest rate and EMI differences over the years, population growth, etc.

Kinds of compound and simple interest question in entrance exams with examples:

• Difference between CI and SI for two years and three years respectively

There is a difference between compound interest and simple interest, considering it for a period of 2 and 3 years. Another kind of question type in this case, is the one where term varies from t to fractions of the time period which is of one year. This implies that the interest rate is not compounded annually but multiple times during a year.

Two year difference: P (r/100)2

Three year difference: P (r/100)2 ({r/100} + 3})

Example: Post office small savings scheme provides interest on money invested. The option is that of interest earned in the form of a simple interest or that compounded annually. Interest earned ranges from 9 percent annual to instruments wherein money is invested for a smaller term and compounded further. Calculate the difference between the interest earned on each of the instruments invested in for an annual term, two years, three years, and half yearly basis.

• Depreciation: Certain goods lose value with time; this holds true for consumer durables, white goods, etc.

Vf      = Vi (1 – r/100)t

Vfj is the final value of goods after taking into account depreciation. Vi is the initial value of         the good. ‘r’ is the rate of interest and ‘t’ is number of years.

Example: This is a simple concept used in accounting. Depreciation of the value of good takes place on a percentage of its absolute value. Compounded over a period of time, the value of the asset can depreciate significantly. Calculate the difference in value of a good today and three year hence.

• Population

P = Po [1+r/100]n

P = Po [1 – r/100]n

Example: Knowing the population in an area is important for implementation of schemes. Po is the initial population. r and n refer to the rate of increase of population and number of years respectively. This value of n may be annual, half yearly or quarterly. Calculate the population of a region given the rate of increase of population.

• Instalments: For simple interest and compound interest

A = (P) + (Pnr)/100

Difference between CI and SI for nth year = Pr/100 [(1+r/100)n-1   – 1]

For Compound Interest

[Increase in amount in nth year]/[increase in amount in (n+1)th year]   = 100 /( 100 + r )

[Decrease in amount in nth year] / [decrease in amount in (n+1) th year] = 100/(100 – r)

Example: Given a compounded rate of interest the difference between the interest earned over a period of years and the inflationary pressure that reduces the value of returns on investment can be calculated using the above stated formula.

Strategies to solve compound and simple interest question in entrance exams:

• Compounding is what this concept stresses upon. Logarithmic tables can also be used if the power n to which the interest rate is raised is high. This makes calculation easier.
• Compound Interest and SI problems are not just about investment and return on investment but can be used in fields where simple or compounded increase in absolute value takes place. Population and revenue are such domains.
• Inflation defines the real returns on investment. In case there is annual compounding of the investment you make, inflation erodes its value. These formulae can be used to calculate appreciation as well as depreciation in value.