Interest Theory

3 properties of a(t)

-usually increasing
-usually continuous
-a(0) = 1

amount function formula and 3 properties

A(t) = K*a(t)
-A(0)= k
-usually increasing and continuous

In formula

A(n)=A(n-1)

effective rate of interest definition and formula (i)

i = amount of money that one unit invested at the beginning of a period will earn during the period where interest is paid at the end of the period

i=a(1)-a(0)

a(t) function definition

a(t) is a function that gives the amount tow which a unit of money invested at time 0 will grow by time t

effective rate of interest alternative formula

(A(1)-A(0))/(A(0)) or replace n with 1 and 0 with n-1

compound interest is the same as?

effective rate of interest

interest definitions

compensation a borrower of capital pays to a lender of capital for its use

-compensates for the loss of capital by the lender while it is loaned to the borrower

alternate formulas for I(t) and A(t)

I(t) = Prt
A(t) = P(1+r/n)^nt

Compare the compound interest graph and the simple interest graph at 0 and 1

between 0 and 1, compound interest curve is below the straight line of simple interest, and afterwards it exceeds simple interest

at t = 1 simple interest = compound interest

v^t and v^-t

v^t = 1/(1+i)^t

v^-t = (1+i)^t

effective rate of discount definition

This is the interest paid at the beginning of the period on balance at the end of the period

Define d

This is the ratio of the amount of interest earned during the period to the amount invested at the end of the period

formulas for d

d=A(n)-A(n-1) over A(n)
d=i*v

d=1-v

1-d is what?

amount at the beginning of the period (v) v= 1-d

write i in terms of d

i = d /(1-d)

v=

v=1/(1+i)
v=1-d

based on your two formulas for v, relate them with appropriate t exponents

(1+i)^t = (1-d)^-t