Compound Interest Formulas

Scenario,FormulaBasicVariables,LetP=Principal,R=RateCompoundedAnnually,Amount=P(1+100R)nCompoundedHalfYearly,Amount=P(1+100R/2)2nCompoundedQuarterly,Amount=P(1+100R/4)4nFractionalTime(e.g.,352years),Amount=P(1+100R)3×(1+10052R)DifferentRatesperYear(R1,R2,R3),Amount=P(1+100R1)(1+100R2)(1+100R3)PresentWorth(ofRs.xduenyearshence),PresentWorth=(1+100R)nxScenario,Formula Basic Variables,”Let P = Principal, R = Rate%, n = Time (years)” Compounded Annually,Amount=P(1+100R​)n Compounded Half-Yearly,Amount=P(1+100R/2​)2n Compounded Quarterly,Amount=P(1+100R/4​)4n “Fractional Time (e.g., 352​ years)”,Amount=P(1+100R​)3×(1+10052​R​) “Different Rates per Year (R1​,R2​,R3​)”,Amount=P(1+100R1​​)(1+100R2​​)(1+100R3​​) Present Worth (of Rs. x due n years hence),Present Worth=(1+100R​)nx​
ScenarioFormula
Basic VariablesLet P = Principal, R = Rate%, n = Time (years)
Compounded Annually$Amount = P \left(1 + \frac{R}{100}\right)^n$
Compounded Half-Yearly$Amount = P \left(1 + \frac{R/2}{100}\right)^{2n}$
Compounded Quarterly$Amount = P \left(1 + \frac{R/4}{100}\right)^{4n}$
Fractional Time (e.g., $3 \frac{2}{5}$ years)$Amount = P \left(1 + \frac{R}{100}\right)^3 \times \left(1 + \frac{\frac{2}{5}R}{100}\right)$
Different Rates per Year ($R_1, R_2, R_3$)$Amount = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right) \left(1 + \frac{R_3}{100}\right)$
Present Worth (of Rs. $x$ due $n$ years hence)$Present\ Worth = \frac{x}{\left(1 + \frac{R}{100}\right)^n}$

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