- #1
issacnewton
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Homework Statement
Hi, I am reading this book called, Introduction to Corporate Finance, by Berk, Demarzo, Harford (second edition). In it they try to explain how to calculate the number of periods in a loan payment formula. Authors give the following equation.
$$ 0 =PV + PMT \times \frac{1}{I/Y}\left( 1 - \frac{1}{(1+I/Y)^N} \right) + \frac{FV}{(1+I/Y)^N} $$
where ##PV## is the present value of annuity, ##PMT## is cash flow or payment per period, and ##I/Y## is the discount rate. I don't understand how they arrive at this formula. Authors are math phobic, I think, as they don't derive difficult formulae from first principles.
Homework Equations
Formula for the annuity.
$$ PV = C \times \frac{1}{r} \left( 1 - \frac{1}{(1+r)^N} \right) $$
where ##C## is annuity for ##N## periods with interest rate ##r##.
The Attempt at a Solution
I am stuck. Any hints would be helpful.