# The difference between simple and compound interest

Thedifference between simple and compound interest

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Thereare differentwaysof calculatinginterestearnedon borrowedmoney.Thequantitative methodshelpin determiningtheamountof moneypaidafter a givenperiod.Differentinstitutionshavedifferentratesof interestthat is paidas either simple interest or compoundinterest.Themajordifferenceis thatsimpleinteresthas an arithmetic growthwhilecompoundinteresthas a geometric growth(Pirnot, 2014).

Institutionsprimarily use compound interest when they are giving out loans thatthey intend to generate high returns. For instance, pension companiesdeposit cash in institutions that pay compound interest to generatehigh profits. Since the intention of compound interest is generatinghigh returns, it is best for the investors. On the other hand,institutions that provide subsidized loans use simple interest rate.For example, members of given institutions or the minority of agiven country are likely to receive subsidized loans.

Insimpleinterest,theinterestgrowthfollowsan arithmetic patternwhereby,therateof interestin calculatedon theinitialprincipal.Forexample,itis calculatedon theinitialmoneyborrowedfrom a financialinstitution.Compoundinterestfollowsa geometric orexponential patternwherebycalculationof interestis in theinitialcapitalandeveryinterestaccumulatedduring theperiod.Forexample,in caseof a loan,interestis chargedon theinitiallyborrowedmoneyandtheinterestaccruedout of theloan(Pirnot, 2014).

Ina realexample,one borrows10, 000 dollarsfrom two financialinstitutions,bothchargingat a rateof 5%per annum fora periodof 3 years.Ifone chargesa simpleinterestandtheotherone a compoundinterest,theamountpaidwill be different.Forthesimpleinterest,theformulaforcalculatinginterestis givenby Principal x ratextime(PxRxT) (Pirnot, 2014).

Intheabovecase,theinterestis givenby 10,000 x 0.05 x 3 that will be equalto 1,500. Theinterestpaidwill be 1,500 dollars.In total,theborrower will paya totalof 11,500 dollarsat theendof theloanperiod.

Wheninterestis in compoundterms,thecalculatingformulais P {(1+i) ^n -1}. Whereby‘P’ is theprincipal,‘I’ is theinterestratechargedannually,andN is theloanperiod.In thisexample,theinterestpaidwill be 10,000{(1+0.05) ^3 -1}.the resultingfigurewill be 1156.25 dollars.Thetotalamountpaidwill be 11,156.25 dollars.

Inconclusion,compoundinterestis favorableto investments.Itcan leadto hugeprofitsin thelong run. Understandingthetwo is importantto anydebtorin orderto knowtheamountpayablewhentheloanperiodelapses.

References

Pirnot,T. L. (2014). *Mathematicsall around (5th ed)*.Pearson Education: Boston