Shortcuts in Quantitative Aptitude for Competitive Exams - Simple & Compound Interest

Shortcuts in Quantitative Aptitude for Competitive Exams – Simple & Compound Interest

Shortcuts in Quantitative Aptitude Reasoning English

INTEREST
Interest is the fixed amount paid on borrowed money.
The sum lent is called the Principal.
The sum of the principal and interest is called the Amount.
Interest is of two kinds :

Simple interest
Compound interest

SIMPLE INTEREST
When interest is calculated on the original principal for any length of time.
It is called simple interest.
REMEMBER

$SimpleInterest =\frac { Principal\times Rate\times Time }{ 100 }$
i.e. S.I. = $\frac { P\times R\times T }{ 100 }$
Principal (P) = $\frac { 100\times S\cdot I }{ R\times T }$
Rate (R) = $\frac { 100\times S\cdot I }{ T\times P }$
Time (T) = $\frac { 100\times S\cdot I }{ P\times R }$
If rate of simple interest differs from year to year, then
Amount = Principal + INTEREST

Shortcut Approach

If $\frac { 1 }{ x }$ part of a certain sum P is lent out at R₁% SI, $\frac { 1 }{ y }$ part is lent out at R2% SI and the remaining $\frac { 1 }{ z }$ part at R3, % SI and this way the interest received by 1, then $p=\frac { 1\times 100 }{ \frac { { R }_{ 1 } }{ x } +\frac { { R }_{ 2 } }{ y } +\frac { { R }_{ 3 } }{ z } }$
If a sum of money becomes n times in T yr at simple interest, then formula for calculating rate of interest will be given as
$R=\frac { 100\left( n-1 \right) }{ T } %$ %
If a sum of money at a certain rate of interest becomes n times in T₁, yr and m times in T2 yr, then formula for T2 will be given as
${ T }_{ 2 }=\left( \frac { m-1 }{ n-1 } \right) \times { T }_{ 1 }$

COMPOUND INTEREST
Money is said to be lent at compound interest when at the end of a year or other fixed period, the interest that has become due is not paid to the lender, but is added to the sum lent, and the amount thus obtained becomes the principal in the next year or period. The process is repeated until the amount for the last period has been found. Hence, When the interest charged after a certain specified time period is added to form new principal for the next time period, the interest is said to be compounded and the total interest accrued is compound interest.

REMEMBER

Amount (A) =
If rate of compound interest differs from year to year, then

Compound interest – when interest is compounded annually but time is in fraction

If time $t\frac { p }{ q }$ years, then

Compound interest – when interest is calculated half-yearly
Since r is calculated half-yearly therefore the rate per cent will become half and the time period will become twice, i.e.,
Rate per cent when interest is paid half-yearly $=\frac { r }{ 2 } %$ %
and time = 2 x time given in years
Hence,

Compound interest – when interest is calculated quarterly
Since 1 year has 4 quarters, therefore rate of interest will become $\frac { 1 }{ 4 }$ th of the rate of interest per annum, and the time period will be 4 times the time given in years Hence, for quarterly interest

Shortcut Approach
Difference between Compound Interest and Simple Interest When T = 2

When T=3

NOTE:
SI and Cl for one year on the same sum and at same rate are equal

Shortcut Approach
If a certain sum at compound interest becomes x times in n₁yr and y times in n2 yr, then

Shortcut Approach
If the population of a city is P and it increases with the rate of R% per annum, then

Population after n yr
$= P\left( 1+\frac { { R }^{ n } }{ 100 } \right)$
Population n year ago
$= \frac { P }{ \left( 1+\frac { { { R }^{ n } } }{ 100 } \right) }$

Note:
If population decreases with the rate of R%, then (-) sign will be used in place of (+) in the above mentioned formula
If the rate of growth per year is R₁%, R2%, R3%,………, Rn%, then Population after n yr

(This formula can also be used, if there is increase/decrease in the price of an article.)

Shortcuts in Quantitative Aptitude for Competitive Exams – Simple & Compound Interest

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