Joanna Adamska-Mieruszewska
International finance
2021/2022
THE TIME VALUE OF MONEY
THE TIME VALUE OF MONEY
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The Interest Rate
Simple Interest
Compound Interest
Annuities (fixed and deffered)
Effective Interest Rate
INTEREST RATE BASICS
▪ Future value (FV): terminal value (the value at
some future time)
▪ Present value (PV): the current value of future
amount of money
▪ Interest rate (i)
▪ Number of time periods (n)
SIMPLE INTEREST
Interest that is paid (earned) on only the original
amount
COMPOUND INTEREST
Interest paid (earned) is periodically added to
the principal
𝐹𝑉 = 𝑃𝑉(1 +
𝑛
𝑖)
ANNUITIES
Fixed deffered annuity: a series of regular
payments are made in order to produce a
lump sum at a later date (retirement nest egg)
Fixed immediate annuity: lump sum is paid to
generate a series of regular payments later
(loans)
Deffered annuity
Future value: the sum of all the payments plus
the interest earned (FVA)
(1 + 𝑖)𝑛 −1
𝐹𝑉𝐴 = 𝐴
𝑖
Deffered annuity
Periodic payment (A): payment necessary to
reach a specific future value target
𝐴(𝐹𝑉𝐴,𝑖,𝑛)
𝐹𝑉𝐴 × 𝑖
=
(1 + 𝑖)𝑛 −1
Immediate Annuities
Flip side of a deffered annuity
Example: an installment loan
Immediate Annuities
Present value (PVA)
1 − (1 + 𝑖)−𝑛
𝑃𝑉𝐴 = 𝐴
𝑖
Immediate Annuities
Amoritization Formula (A or PMT)
𝐴(𝑃𝑉𝐴,𝑖,𝑛)
𝑃𝑉𝐴 × 𝑖
=
1 − (1 + 𝑖)−𝑛
ANNUITIES
Ordinary annuity
A sequence of equal payments made or
received at the end of equal time periods
Ex: regular deopsits; credit card debt; trust fund;
scholarship, etc.
ANNUITIES
Annuity Due - a series of equal payments
occurring at the beginning of each period
ANNUITIES:
THE LOTTERY WINNER’S DILEMMA
How does a present value compare with a
future value of N annual payments?
▪ risk (i)
▪ psychological ad sociological aaspects to the
decision (self-control, friends, relatives)
▪ current financial situation