Financial accounting summary year 2
period 3
, Chapter 5 time value of money
Learning goal 1 discuss the role of time value in finance, the use of computational tools, and the basic
patterns of cash flow
Learning goal 2 understand the concepts of future value and present value, their calculation for
single cash flow amounts and the relationship between them
Learning goal 3 find the future value and the present value of both and ordinary annuity and an
annuity due, and find the present value of a perpetuity.
Learning goal 4 calculate both the future value and the present value of a mixed stream of cash flows
Learning goal 5 understand the effect that compounding interest more frequently than annually has
on future value and on the effective annual rate of interest
Learning goal 6 describe the procedures involved in (1) determining deposits needed to accumulate a
future sum (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown
number of periods
5.1 the role of time value in finance
Future value versus present value
Timeline a horizontal line on which time appears at the leftmost end and future periods are marked
from left to right; can be used to depict investment cash flows.
Basic patterns of cash flow
Single amount: a lump sum either currently held or expected at some future date
Annuity: a level periodic stream of cash flow.
Mixed stream: a stream of cash flow that is not an annuity; a steam of unequal periodic cash flows
that reflect no particular pattern.
5.2 single amounts
Future value of a single amount
Future value the value on some future date of money that you invest today
Compound interest interest that is earned on a given deposit and has become part of the principle at
the end of a specified period.
Principal the amount of money which interest is paid
n
Future value = FV n=PV 0 X (1+r )
FV = future value after n periods
PV = initial principal, or present value when time = 0
R = annual rate of interest
N = number of periods (typically years) that the money remains invested
period 3
, Chapter 5 time value of money
Learning goal 1 discuss the role of time value in finance, the use of computational tools, and the basic
patterns of cash flow
Learning goal 2 understand the concepts of future value and present value, their calculation for
single cash flow amounts and the relationship between them
Learning goal 3 find the future value and the present value of both and ordinary annuity and an
annuity due, and find the present value of a perpetuity.
Learning goal 4 calculate both the future value and the present value of a mixed stream of cash flows
Learning goal 5 understand the effect that compounding interest more frequently than annually has
on future value and on the effective annual rate of interest
Learning goal 6 describe the procedures involved in (1) determining deposits needed to accumulate a
future sum (2) loan amortization, (3) finding interest or growth rates, and (4) finding an unknown
number of periods
5.1 the role of time value in finance
Future value versus present value
Timeline a horizontal line on which time appears at the leftmost end and future periods are marked
from left to right; can be used to depict investment cash flows.
Basic patterns of cash flow
Single amount: a lump sum either currently held or expected at some future date
Annuity: a level periodic stream of cash flow.
Mixed stream: a stream of cash flow that is not an annuity; a steam of unequal periodic cash flows
that reflect no particular pattern.
5.2 single amounts
Future value of a single amount
Future value the value on some future date of money that you invest today
Compound interest interest that is earned on a given deposit and has become part of the principle at
the end of a specified period.
Principal the amount of money which interest is paid
n
Future value = FV n=PV 0 X (1+r )
FV = future value after n periods
PV = initial principal, or present value when time = 0
R = annual rate of interest
N = number of periods (typically years) that the money remains invested
