Financial Equations: Math 181

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Revised October 16, 2013 Some images on this page have been generated via AsciiMathML.js.
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Simple Interest

Find Interest Amount:
`Int = (PV)(r)(t)`

Find Future Value:
`FV = PV + Int`
`FV = PV + PV(r)(t)`
`FV = PV(1 +rt)`

Find Present Value:
`PV = FV(1/(1+rt))`
`PV =(FV)/(1+rt)`

Find Rate:
`r = ((FV)/(PV)-1)(1/t)`

Find Time:
`t = ((FV)/(PV)-1)(1/r)`

Compound Interest

Find Future Value:
`FV = PV(1 +r/m)^(mt)` where `r`=annual rate, `m`=times per year, `t`=number of years
`FV = PV(1 + i)^n` where `i=r/m` is rate within each period and `n=mt` is number of compounding periods

Find Present Value:
`PV = (FV)/((1+r/m)^(mt))`
`PV = FV(1+r/m)^(-mt)`
`PV = (FV)/((1 + i)^n`
`PV = FV(1 +i)^(-n)`

Find Annual Rate:
`r = (((FV)/(PV))^(1/(mt))-1)m`

Find Number of Years:
`t = log( (FV)/(PV) )/(m log(1+r/m))`

Ordinary Annuities (Sinking Fund)

Find Future Value:
`FV = PMT( ((1 + i)^n - 1)/i)`

Find Payment (Rent):
`PMT = FV(i/((i + i)^n - 1))`

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