Finance Chapter 5 Terms + Equations

A simple interest rate that regulators require banks to state on all consumer loans.

APR = periodic rate (r) x # of periods per year (m)

Ex: 50 bps per month is 6% APR

The annualized interest rate that reflects the true cost or return over one year by fully accounting for compounding.

APY/EAR = ((1+r)^m) - 1
- r = APR/m

Ex: A stated rate of 6% APR with daily compounding is equivalent to an APY of 6.18%, rounded to the basis point (hundredth).

APR = m*((1+APY)^1/m) − 1

Single period concept which best predicts what the next random one-period return will be

More than the geometric average (unless same)

Only use for distributions/probabilities

The average compound return earned per year over a multiyear period

Less than the arithmetic average (unless same)

rg = ((FV/PV)^1/t) - 1

An increase/decrease in an asset's price over a time period

The component of an asset's total return that results from a price change

(End Price - Beg. Price) / Beg. Price

Calculates and pays interest at every insignificantly small time interval

Immediately begins earning interest on interest

Maximum possible effective rate for a given APR

APY = (e^APR) - 1

FV = PV * (e^APR*t)

PV = FV * (e^-APR*t)

APR = ln(FV/PV) / t

Can swap APR and t in order to solve for t

The return from dividends relative to the stocks price

The change in an asset's price plus any cash income the asset produces over a certain time interval

(End Price - Beg. Price) + Cash Income

A low-frequency rate that is equivalent to a high-frequency rate

Ex: an effective annual rate of 12.682503% (low-frequency) = 1% per month (high-frequency)

The rate of return an investment produces

The discount rate that makes a project's NPV = 0

Accept if IRR > Hurdle Rate (Minimum Return Rate), Otherwise Reject

A company's minimum acceptable rate of return for an investment or project, given the perceived riskiness of the endeavor

Same as required return

Assists in applying the IRR rule or a discount rate in the net present value rule.

Income you earn each year (dividends/interest) divided by the price you paid for the investment

-The growth rate per compounding period defined by the contract (decimal form)

Must match the time period of cashflows

Ex: 10 bps per week

# of compounding periods per year

# of periods

Must match the time period the contract uses for its interest rate.