Finance Ch.4

is the value today of a future payment, or stream of payments,
discounted at the appropriate rate of interest.  It is also the beginning amount that will grow to some future value.

an investment is the rate of return available on the best
alternative investment of similar risk

is the periodic interest rate that an account pays and is the dollars of interest earned each period.

is the ending amount in an account, where n is the number of periods the moneyis left in the account. PVAn is the value today of a future stream of equal payments (an annuity) and FVAn is the ending value of a stream of equal payments, where n is the number of payments of the annuity. PMT is equal to the dollar amount of an equal, or constant cash flow (an annuity). In the EAR equation, m is used to denote the number of compounding periods per year, while iNom is the nominal, or quoted, interest rate.

is a series of payments of a fixed amount for a specified number of periods.

as opposed to an annuity, consists of one payment
occurring now or at some future time.

flow can be an inflow (a receipt) or an outflow (a deposit, a cost, or an amount paid). We distinguish between the terms cash flow and PMT. We use the term cash flow for uneven streams, while we use the term PMT for annuities, or constant payment amounts.

is a series of cash flows in which the amount varies from one period to the next. The PV(or FVn) of an uneven payment stream is merely the sum of the present values (or future
values) of each individual payment.

has payments occurring at the end of each period, The payment period must be equal to the compounding period.

has payments occurring at the beginning of each period.
The payment period must be equal to the compounding period.

is a series of payments of a fixed amount that last indefinitely. In other words, it is an annuity where n equals infinity.

is a deposit, a cost, or an amount paid, while an inflow is a receipt

is an important tool used in time value of money analysis; it is a graphical representation which is used to show the timing of cash flows.

is the future value of an uneven cash flow stream.

is the process of finding the future value of a single payment or series of payments.

is the process of finding the present value of a single
payment or series of payments; it is the reverse of compounding.

interest is paid once a year.

interest is paid 2, 4, 12, and 365 times per year
respectively. When compounding occurs more frequently than once a year, you earn interest on interest more often, thus increasing the future value. The more frequent the
compounding, the higher the future value.

is the rate that, under annual compounding, would have
produced the same future value at the end of 1 year as was produced by more frequent
compounding, say quarterly.

is the rate of interest stated in a contract

occurs annually, the effective annual rate and the nominal rate are the same.

is also called the annual percentage rate, or APR.

is the rate charged by a lender or paid by a borrower each period. It can be a rate per year, per 6-
month period, per quarter, per month, per day, or per any other time interval (usually
one year or less).

is a table that breaks down the periodic fixed payment of an
installment loan into its principal and interest components. 
The principal component of each payment reduces the remaining principal balance. The interest component is
the interest payment on the beginning-of-period principal balance. An amortized loan is one that is repaid in equal periodic amounts (or "killed off" over time).

EAR or EFF

PMT/I =

Nominal quoted interest rate

Number of compounding periods per year

Number of Years

PVA-due = PVA-ordinary(1+I)

r=[(1+r-nominal)/(1 + inflation)]-1.0

EAR = (1 + Iperiodic)^M-1.0

Periodic rate Iper= Inominal/M

FV= FV1 "the number 1 means year 1"  FV(1+I)

=PV(1+I)^N

to find future values

I= [FV(N)/PV]^(1/N) - 1

FVA(N)= PMT[(1+I)^N/I - 1/I]=

PVA(N) = PMT[1/I - 1/I(1+I)^N]