A12 Interest Accumlation Part 2

Question 1

Hhoow can you accumlate from time t_1 to time t_2 using the accumulation function a(t)

Answer 1

a(t_2)/a(t_1)

Question 2

what is the meaning of the effective rate of interest, i_t?

Answer 2

i_t is the amount of interest earned in the t-th period divided by the amount invested at the beginning of the period.

or

The effective rate of interest, i, is the 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.

Question 3

what does the term effective mean?

Answer 3

The term “effective” is used for rates of interest in which interest is paid once per measurement period

Question 3

express the accumulation factor for the t-th period in terms of i_t, the effective rate of interest for the t-th period.

Answer 3

1 + i_t

Question 4

give the formula for the effective rate of interest i_t in terms of the accumulation function a(t)

Answer 4

i_t = (a(t) - a(t-1))/a(t-1)

Question 5

what is accomplished by multiplying by the accumulation factor for the t-th period?

Answer 5

A money value at time t-1 is accumulated forward to it’s value at time t.

Question 6

express the accumulationf actor for the t-th period in terms of a(t), the accumulation function?

Answer 6

a(t)/a(t-1) is an accumulation factor for the period from time t-1 to time t

Question 7

how do you find interest?

Answer 7

final bal - beginning bal