Theory of Interest module 1 vocab/formulas

period

the unit in which time is measured, such as one year

principal

the amount of money at the beginning of the period

accumulated value

the final amount of money after a period of time

interest

accumulated value - principal

accumulation function, a(t)

describes the accumalated value at time t >= 0 of an investment of 1 (one dollar) at time t=0.

amount function, A(t)

gives the accumulated value of an initial investment of k at time t. A(t) = ka(t)

I_t, interest earned during the t^th period from the date of investment

I_t = A(t) - A(t-1) for t=1,2…

discount function, v(t)

gives the amount that must be invested at the beginning of the period to obtain an accumulated value of 1 at time t >= 0, v(t) = 1/a(t)

effective interest rate i_t

the amount of money that $1 invested at the beginning of period t will earn during period t. i_t = [A(t) - A(t-1)] / [A(t-1)] = i_t/A(t-1)

effective discount rate d_t

the amount of money that $1 at the end of period t earns during period t. d_t = [A(t) - A(t-1)] / [A(t)] = i_t/A(t)

simple interest

method of accrual such that the amount of interest earned during each period is constant. a(t) = 1 + it v(t) = 1/a(t)

simplified interest formula in simple interest

interest = k * it