Finance Formulas

gs

future value

FV = PV * (1+r)^n

present value

PV = FV * 1/[(1+r)^n]

can be found simply by rearranging FV formula

yield

r = [(FV/PV)^1/n] - 1

value of standard perpetuity

PV = PMT / r

e.g. pricing of stocks (calculated using dividend amount)

value of growing perpetuity

PV = PMT / (r-g)

where g is rate of growth of the payment

value of standard annuity

PV = [PMT / r] * [1 - (1/(1+r)^n)]

is essentially the difference between two perpetuities, one of which begins at time 0 and the second of which starts at time n

value of zero-coupon bond

PV = FV * 1/[(1+r)^n]

(same as present value formula since there are no intermediary payments)

value of coupon bond

PV of annuity + PV of final (maturity) payment; can simply be calculated using Excel’s PV formula

effective interest rate (EIR; or annual equivalent rate, AER)

EIR = [(1 + periodic rate) ^ m] - 1

where m is the number of compounding periods per year (e.g. if interest is compounded quarterly, m = 4)