A13 Present Value Pt 1

Question 1

express the discount function a_1 (t), in terms of the accumulation function a(t).

Answer 1

a^1 (t) = 1/a(t)

Question 2

what are four ways (involving a(t), i_t, d_t, and v_t) to discount a money value from time t to time t-1?

Answer 2

Multiply by a(t-1)/a(t)
Divide by 1+i_t
Multiply by 1-d_t
Multiply by v_t

Question 3

what is the meaning of the discount function, a^-1 (t)?

Answer 3

It is the value at time 0 of $1 at time t

Question 4

what is the meaning of the effective rate of discount, d_t?

Answer 4

d_t is the amount of interest earned in the t-th period divided by the amount invested at the end of the period

Question 5

give the formula for the effective rate of discount d_t in terms of the accumulation function a(t) and what does it mean?

Answer 5

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

d_t equals the amount of interest earned in period t divided by the amount invested at the end of the period.

Question 6

express the discount factor for the t-th period, v_t, in terms of d_t, the effective rate of discount for the t-th period.

Answer 6

v_t = 1 - d_t

discount factor equals 1 - effective rate of discount.

Question 7

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

Answer 7

v_t = 1/(1+i_t)

Question 8

What is accomplished by multiplying by the discount factor for the t-th period?

Answer 8

A money value at time t is discounted backward to its value at t-1

Question 9

what are four ways (involving a(t), i_t, d_t and v_t) to accumulate a money value from time t-1 to time t?

Answer 9

Multiply by a(t)/a(t-1)
Multiply by 1+i_t
Divide by 1-d_t
Divide by v_t

Question 10

what is the present value?

Answer 10

is that value of the money right now.