[Verse 1] Sarah's planning for retirement, needs to understand How her monthly payments grow with compound interest in hand She'll pay a thousand every year for twenty years ahead But when's the payment due, she asks, beginning or end? [Chorus] Present value, future value, streams of cash that flow PMT times the factor, that's the way the numbers go Ordinary waits till end, annuity due starts now Perpetuity goes forever, let me show you how PV equals PMT over R, when payments never cease Time value calculations bring your financial peace [Verse 2] If payments come at period's end, ordinary's the name PMT times bracket one minus one plus R to negative N, then divide by R just the same But if the payment starts today, annuity due we call Multiply by one plus R, and you'll have it all [Chorus] Present value, future value, streams of cash that flow PMT times the factor, that's the way the numbers go Ordinary waits till end, annuity due starts now Perpetuity goes forever, let me show you how PV equals PMT over R, when payments never cease Time value calculations bring your financial peace [Bridge] When the payments never end, perpetuity's the key No need for complex formulas, just PMT over R you see But remember interest rates must stay above zero line For perpetual payments to make mathematical sense in time [Verse 3] Future value tells us where our money's going to be PMT times bracket one plus R to N minus one, divide by R eventually Whether saving for a house or planning for your needs Understanding payment streams plants financial seeds [Chorus] Present value, future value, streams of cash that flow PMT times the factor, that's the way the numbers go Ordinary waits till end, annuity due starts now Perpetuity goes forever, let me show you how PV equals PMT over R, when payments never cease Time value calculations bring your financial peace [Outro] From CPA studies to real world application Payment streams and present values build your foundation Remember timing matters in every calculation Annuities and perpetuities for financial liberation
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