Glossary¶

accumulation function

A function that describes how much as single unit of currency grows over time. It is a special case of the amount function, where the amount invested is restricted to be one unit of currency.

amount function

A function that describes how much an invested amount of money grows over time.

annual percentage rate (APR)

The nominal interest rate.

annual percentage yield (APY)

The annual effective interest rate.

annuity

A series of payments made at specified intervals for a fixed or contingent period.

annuity-due

An annuity in which the payments occur at the beginning of each payment period.

annuity-immediate

An annuity in which the payments occur at the end of each payment period.

balloon payment

An adjustment to the value of the final payment of a loan so that it can occur on the previous integral payment period.

basic annuity-due

An annuity-due that pays 1 at the beginning of each period.

basic annuity-immediate

An annuity-immediate that pays 1 at the end of each period.

basic perpetuity-due

A perpetuity-due that pays 1 at the beginning of each period.

basic perpetuity-immediate

A perpetuity-immediate that pays 1 at the end of each period.

bond

A financial instrument that entities, called bond issuers, can use to borrow money from other entities, called bondholders.

compound interest

A geometric pattern of money growth in which interest earned is reinvested at the rate of interest.

deferred annuity

A type of annuity whose first payment begins more than one payment period later than its present valuation date.

discount

The amount of money that must be paid up front on a loan.

discount function

The reciprocal of the accumulation function:

$v(t) = \frac{1}{a(t)}$

dollar-weighted yield rate

See yield rate

drop payment

An adjustment to the amount of the final payment of a loan so that it can occur on the next integral payment period.

effective rate of interest

A measurement of money growth equal to the percentage change in the value of an investment between two time periods:

$i_{[t_1, t_2]} = \frac{a(t_2) - a(t_1)}{a(t_1)}$

force of interest

The limit of the nominal interest or discount rate as the compounding frequency approaches infinity.

growth

The change in the value of money over time.

interest earned

A measurement of money growth equal to the change in the value of an investment between two time periods:

$A_K(t_2) - A_K(t_1).$

internal rate of return

See yield rate

modified coupon rate

The bond coupon rate expressed in terms of the redemption amount.

net present value (NPV)

The sum of the present value of a stream of returns:

$\sum_{k=0}^n R_k v(t_k)$

nominal discount rate

The discount rate $d^{(m)}$ compounded $m$ times per year.

nominal interest rate

The interest rate $i^{(m)}$ compounded $m$ times per year.

retrospective method

A way of calculating the outstanding loan balance at time $t$ by subtracting the accumulated value of the payments to date from the accumulated value of the principal.

par-value bond

A bond whose face value equals its redemption amount.

perpetuity

An annuity with an infinite number of payments

perpetuity-due

A perpetuity that makes payments at the beginning of each period.

perpetuity-immediate

A perpetuity that makes payments at the end of each period.

principal

An initial investment of money.
The original amount of a loan that must be paid back.

prospective method

A method of calculating the outstanding loan balance at a point in time $t$ that sums up the remaining payments and discounts them to time $t$ .

present value

The value today of money to be received in the future.

simple interest

A linear pattern of money growth in which interest earned is a fixed amount per time period.

yield rate

The rate that solves the time $\tau$ equation of value.