Module 1: Time Value of Money

Question 1

what is a(0)

Answer 1

1

Question 2

what is A(t)

Answer 2

k*a(t) or k/v(t)

Question 3

how to calculate interest earned?

Answer 3

A(n)-A(n-1)

Question 4

exact simple interest method

Answer 4

ignores leap years, assume every year has 365 days, t = # of days/365

Question 5

ordinary simple interest method

Answer 5

approximates by rounding full months to 30 days each and each year to 12 x 30 = 360 days, t = approximate # of days/360

Question 6

bankers rule

Answer 6

counts # of days exactly but uses 360 as # of days in a year, t = number of days/360

Question 7

a(t) for simple interest

Answer 7

1 + it

Question 8

v(t) for simple interest

Answer 8

1 - it

Question 9

a(t) for compound interest

Answer 9

(1+i)^t, t>=0

Question 10

v(t) for compound interest

Answer 10

(1-i)^t

Question 11

what happens to a(t) between 0

Answer 11

a(t) for simple interest > a(t) for compound interest

Question 12

what happens to a(t) at t = 0 and t = 1

Answer 12

a(t) for simple interest = a(t) for compound interest

Question 13

Effective interest rate of period (t1, t2)

Answer 13

i[t1, t2] = interest earned during period/amount at beginning of period = A(t2) - A(t1)/A(t1) = a(t2)-a(t1)/a(t1)

Question 14

what is the accumulation factor

Answer 14

(1+i). This is the growth factor

Question 15

effective rate of discount in nth year

Answer 15

=discount (interest) earned in nth year / amount at the end of nth year
= A(n) - A(n-1) / A(n)
= a(n) - a(n-1) / a(n)

Question 16

EIR

Answer 16

(1+i/n)^n - 1

Question 17

EDR

Answer 17

(1-i/n)^-n - 1

Question 18

a(t) when t < 0

Answer 18

a(t) < 1

Question 19

a(t) when t > 0

Answer 19

a(t) > 1

Question 20

v(t) for simple discount

Answer 20

v(t) = 1 - dt, 0 <= t < 1/d

Question 21

are effective rates with simple interest increasing/decreasing with time?

Answer 21

decreasing

Question 22

are effective rates with simple discount increasing/decreasing with time?

Answer 22

increasing

Question 23

v(t) for compound discount

Answer 23

(1-d)^t for t>=0

Question 24

effective rate formula for i

Answer 24

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

Question 25

what is i^(m)

Answer 25

annual effective rate compounded m times

Question 26

what is i^(m)/m

Answer 26

“quarterly” effective rate

Question 27

effective rate formula for d

Answer 27

1-(1-d/m)^m

Question 28

going from effective interest rate to discount rate

Answer 28

i = d / (1-d)

Question 29

going from effective discount rate to interest rate

Answer 29

d = i / (1 + i)

Question 30

how does I^m change as m increases

Answer 30

decreases at a decreasing rate

Question 31

how does d^m change as m increases

Answer 31

increases at a decreasing rate

Question 32

how does i^m and d^m change as m changes

Answer 32

they are both approaching the same limit, i^m as m is small and d^m as m is big

Question 33

what is δ

Answer 33

constant force of interest; annual nominal rate of interest with continuous compounding

Question 34

formula for δ

Answer 34

= i^(infinity) = ln(1+i)

Question 35

what is δt

Answer 35

instantaneous relative change in accumulation function

Question 36

what is a(t) for δ

Answer 36

a(t) = e^δt

Question 37

what is a(t) for δt

Answer 37

a(t) = e^(integral from time 1 to time 2 of δt)

Question 38

what is p(t)

Answer 38

price index function

Question 39

what is ã

Answer 39

real accumulation function

Question 40

what is p(0)

Answer 40

1

Question 41

formula for real accumulation function ã

Answer 41

ã = a(t) / p(t)

Question 42

what is p(t) formula

Answer 42

(1+r)^t

Question 43

what is ã(t) formula

Answer 43

(1 + ĭ)^t

Question 44

what is r

Answer 44

annual effective rate of inflation

Question 45

what is ĭ

Answer 45

annual effective rate of “real” interest

Question 46

what is ĭ formula

Answer 46

i - r / 1 + r

Question 47

how to solve for ĭ^(m)

Answer 47

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

Question 48

what does payments of $100 at time t mean?

Answer 48

$100 / (1+i)^t

Question 49

what is i^(infinity) = δ formula in general

Answer 49

derivative of a(t) / a(t) = d/dt of ln(a(t))