4001ECN: Interest Rates and Annuities Vocabulary

Vocabulary flashcards covering core interest rate concepts, compounding, geometric series, annuities, and perpetuities from lecture notes.

Time Value of Money

The financial principle that $1\,\text{pound}$ today is worth more than $1\,\text{pound}$ tomorrow.

Simple Interest

Interest accrued on a given sum in a set time period that is earned ONLY on the original investment (principal) and is not reinvested.

Compound Interest

Interest that is reinvested by being added to the original investment every time it accrues, so that interest is earned on previously earned interest.

Principal (Initial Investment)

The original sum of money invested or borrowed, represented by $A$ in financial accumulation formulas.

Final Value Formula ($F$)

The formula $F = A(1 + i)^n$, where $A$ is the initial present value, $i$ is the interest rate as a decimal fraction, and $n$ is the number of periods.

Annual Equivalent Rate (AER)

The official annual interest rate for savings accounts that shows how much interest is earned on savings for one year, taking compound interest into account to allow easy comparisons.

Annual Percentage Rate (APR)

The official quote for the cost of borrowing for one year, including the cost of debt and any additional fees related to a loan, taking compound interest into account.

AER / APR Monthly Compounding Formula

The formula $\text{AER} = (1 + i_m)^{12} - 1$ or $\text{APR} = (1 + i_m)^{12} - 1$, where $i_m$ represents the monthly interest rate.

Daily Interest Rate Formula ($i_d$)

The part-year interest rate formula derived from AER or APR:

i_d = \root{365}\tightlist{\text{AER} + 1} - 1.

Geometric Series

A sequence starting with an initial term where each successive term is equal to the previous term multiplied by a common ratio.

General Form of a Geometric Series

The sequence a, ak, ak^2, \reflectbox{\text{\ttdots}}, ak^{n-1} , where $a$ is the initial term, $k$ is the common ratio, and $n$ is the total number of terms.

Sum of a Geometric Series Formula ($\text{GP}_n$)

The sum formula

$\text{GP}_n = \frac{a(1 - k^n)}{1 - k}$,

where $a$ is the initial term, $k$ is the common ratio, and $n$ is the number of terms.

Sum of a perpetual annuity

Annuity

A financial investment that gives a fixed return ($R$) that is the same in each period over a specified period of time.

Annuity Price Formula ($\text{PV}$)

The present value formula used to calculate the price of an annuity:

$\text{PV} = \frac{R[1 - (1 + i)^{-n}]}{i}$ ,

where $R$ is the annual payment, $i$ is the interest rate, and $n$ is the number of years.

Annuity Annual Income Formula ($R$)

The formula used to determine the level of annual income an annuity provides for a specific present value sum:

$R = \frac{i \times \text{PV}}{1 - (1 + i)^{-n}}$.

Perpetual Annuity (Perpetuity)

A form of annuity that promises a fixed annual monetary return forever (n \rightarrow \text{\textinf}).

Perpetuity Price Formula ($\text{PV}$)

The formula for the present value of a perpetual annuity paying fixed annual return $R$ starting in 12 months at interest rate $i$, given by

$\text{PV} = \frac{R}{i}$.