Topic 1.1 Interest Rate Definitions & Annuities

Flashcards covering interest rate definitions, accumulation, discounting, nominal and effective rates, force of interest, simple interest, the time value of money, inflation, annuities, and their actuarial notation based on lecture notes.

Amount function (A(t))

The amount of money at time t, assuming initial deposit at time zero and no additional deposits or withdrawals.

I(t)

The amount of interest earned in the tth period, calculated as A(t) - A(t - 1).

Effective rate of interest (it)

The interest earned during period t divided by the amount invested at the beginning of period t (i_t = I(t) / A(t - 1)).

Present value

The current worth of an investment.

Accumulated value

What the present value grows to over time; also known as compounding.

Discounting

The process of calculating present value from a future value.

Accumulating

The process of calculating future value from a present value.

Discount factor (v)

A factor used to bring a future value back one year, represented as v = 1 / (1 + i) or v = 1 - d.

Effective rate of discount (dt)

The interest earned during period t measured based on the end-of-the-period amount function (d_t = I(t) / A(t)).

Equivalent rates

Two rates that measure the same growth over a specified period.

Nominal Rate of Interest (i^(m))

An annual interest rate stated with a specific number of compounding periods (m) per year, calculated as m times the effective rate per compounding period.

Rule of 72

An approximation stating that the annual effective interest rate multiplied by the number of years to double an investment approximately equals 72.

Nominal discount rates (d^(m))

An annual discount rate where interest is compounded (discounted) 'm' times a year, such that (1 - d^(m)/m)^m = (1 - d).

Accumulation function (a(t))

A special case of the amount function where the initial investment is $1.

Force of interest (δ)

The nominal rate of interest as the number of compounding periods (m) approaches infinity, calculated as ln(1 + i), representing continuous compounding.

Simple interest

An interest method that creates a linear growth function, where interest is earned only on the original investment amount.

Simple discount

An interest method where the accumulation function is a(t) = 1 / (1 - dt) for 0 < t <= 1.

Varying force of interest (δ_t)

A force of interest that changes over time, defined as a'(t) / a(t).

Time value of money

The concept that money received now is worth more than receiving it in the future due to its earning potential.

Equation of value

An equation used to equate interest-adjusted inflows and outflows at a common comparison date.

Inflation

A general increase in the prices of goods and services in an economy.

Rate of inflation (r)

The rate that measures the overall increase in the price of goods.

Nominal interest rate (market interest rate)

An interest rate that is not adjusted for inflation.

Real interest rate (i_real)

An interest rate that is earned net of inflation, calculated as (i - r) / (1 + r).

Annuity

A series of payments made at regular intervals.

Level annuities

Annuities where all payments are of the same amount.

a_n|i

The present value of an annuity of 'n' payments of $1, where the comparison date is one period before the first payment.

s_n|i

The accumulated value of a level annuity of 'n' payments of $1, valued on the date of the last payment.

Annuity immediate

An annuity where the comparison date for its present value is one period before the first payment.