Simple & Compound Interest, and Population Growth Tricks and Formulas

Simple Interest

LetPrinciple=P,Rate=R%perannumandTime=Tyears.Then,

  • S.I.=(P×R×T)/100

  • P=(100×S.I.)/(R×T),

  • R=(100×S.I.)/(P×T),

  • T=(100×S.I.)/(P×R).

Compound Interest

LetPrinciple=P,Rate=R%perannumandTime=Tyears . Then,

  • When interest is compounded Annually,

    Amount =P(1+R/100)N

  • When interest is compounded Half-yearly:

    Amount=P(1+R/2/100)2N

  • When interest is compounded Quarterly:

    Amount=P(1+R/4/100)4N

  • When interest is compounded Annually, but the time is in fraction, say 3 years.

    Then, Amount=P(1+R/100)3×(1+R/100)

  • When Rates are different for different years, say R1%,R2%,R3%for1st,2nd,and3rdyear respectively,

    Then, Amount=P(1+R1/100)(1+R2/100)(1+R3/100)

  • Present worth of Rs. x due n years hence is given by: Present Worth=x/(1+R/100)n

Population Formula

P'×(1±r100)nP

[Here,P=Originalpopulation,P=populationafternyears,r=rateofannualchange]

Depreciation Formula

P'×(1r100)n

[Here,P=originalvalue,P=finalvalueafternyears,r%=rateofannualdepreciation]

Growth

  • AbsoluteGrowth=FinalValueInitialValue

  • Growthrateforayear=FinalValueInitialValueInitialValue×100

  • S.A.G.R.orA.A.G.R.=GrowthRateNumberofYears×100

  • C.A.G.R.=(FinalValueInitialValue)1NumberofYears1

[Here, S. A. G. R. = Simple Annual Growth Rate, A. A. G. R. = Average Annual Growth Rate and C. A. G. R. = Compound Annual Growth Rate]