Exam FM

I(t)

Interest earned at a time, t. = A(t)-A(t-1)

Time diagram (def'n)

compares cash inflows and outflows using a similar comparison date to accumulate/ discount values toward

Generally, it is safe to assume that effective interest rates on exam will grow at a '_________' rate

constant

Effective rate of discount

d_t= [(A(t)-A(t-1)]/A(t) the amount of discount divided by the amount at the end of the discount period

constant growth in effective interest implies graphically that the amount function is _____ & ______.

exponential, concave up

Nominal Rate definition if effective semiannual rate is 5%, calculate the nominal annual rate and the effective annual rate

given an effective rate for time period, the nominal rate is the effective rate multiplied by the number of converted time periods ie; if effective rate is 5 % then the nominal rate is 10% annually, even though the true effective annual rate would be 10.25%

Formula for the effective interest rate I as a function of nominal interest rate i-upper-m

i= (1 + i(m)/m)^m - 1

Equivalent Rates Definition rates i and j are st...

the accumulation function for i is equal to the accumulation function for j

discount factor, v (formula)

1 v = ------- 1+i

The relationship between the set of all possible interest rates and all possible discount rates between two adjacent time periods is

1-1

3 things to immediately circle and understand on any problem

1. Cash inflows and outflows 2. Interest rate unit (annual versus monthly, etc...) 3. Time

Process of drawing a time diagram

1. Identify cash flows 2. Separate outflows from inflows -put outflows on top -put inflows on bottom 3. Set a comparison date

State the two interpretations of discount rate, d

1. rate at which the future value of investment tends into the present value 2. the interest rate paid in advance that is equivalent to the interest rate paid in arrears

Give the 4 equivalent rate formulas 1. General Formula 2. discount rate as function of effective interest rate 3. discount rate as function fo effective interest rate and discount factor 4. effective interest rate as function of discount factor

1. v = 1/(1+i) = d-1 2. d= i/(1+i) 3. d-i*v 4. i=d/(1-d)

Given a positive interest rate, i, the discount rate, d, is st i __ d

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Amount Function formula as a function of effective interest rate from initial investment (GIVEN CONSTANT EFFECTIVE RATE)

A(t) = A(0) * ( 1 + I(t) )^t

Amount Function formula as a function of effective interest rate from specified time period, k. (GIVEN CONSTANT EFFECTIVE RATE)

A(t) = A(k) * ( 1 + I(t) )^(t-k)

Amount Function formula as a function of effective interest rate and the immediately previous time period

A(t) = A(t-1) * ( 1 + I(t) )

Amount Function Formula as function of constant discount rate

A(t)=A(k)*((1−d)^−(t−k))

You are given the following amount function: A(t)=t2+100A(t)=t2+100 Suppose $50 was invested at t = 4. What would be its accumulated value at t = 6?

AV=50*(136/116) = 58.62

AV

Accumulated Value: how fast a fund grows between two time periods A(t) = ----- * Initial Investment A(n)

A(t)

Amount function: measures amount in a fund at time t given initial investment and NO future investments

James invests $100 in a bank. The fund earns an annual effective interest rate of 10%. Calculate the fund accumulation at the end of six months.

Given that rate is ANNUAL EFFECTIVE, t=12/6=0.5 Then , A(0.5) = A(0) * (1.10)^0.5 = 104.88

Rule of 72

The number of years it takes for a certain amount to double in value is equal to 72 divided by its annual rate of interest.

Effective Rate of Interest (def'n and formula)

The interest earned in time period, t, divided by the amount invested at the BEGINNING of time period, t . I(t) A(t)-A(t-1) = ------- = ------------- A(t-1) A(t-1)