FIN 300
Fundamentals of Finance
Time Value of Money
Lump-Sum Problems
Chapters 5 & 6
1
FIN 300 - TVM Lump Sum

Compound Interest
•
Let’s invest $100 for 2 years, earning a 10%
interest rate (or, return) per year
How much will we have after 2 years?
Answer……..
FIN 300 - TVM Lump Sum
2

Compound Interest
Answer is $121!
Let’s break down the math…
•
Start out at t=0, invest $100
•
After 1 year, we have the original $100 + 10% interest
on the $100 = $100 + $10 = $110
•
Assume we invest the full $110 again for the second
year
(no withdrawal)
•
After 2 years, we have the original $100, the 1
st
year’s interest of $10, the 2
nd
year’s 10% interest on
the original $100 investment (which gives us $10 in
additional interest), and finally, the 2
nd
year’s 10 %
interest on the 1
st
year’s $10 in interest (which adds
$1
)
FIN 300 - TVM Lump Sum
3

Compound Interest
•
Let’s break down the $121 amount…..
–
The $100 amount is called?
–
The $21 amount is called?
–
The $20 amount is called?
–
The $1 amount is called?
–
The $121 is called?
FIN 300 - TVM Lump Sum
4

Compound Interest
•
The
$100
amount is the
principal,
aka. the
present value (PV)
•
The
$21
amount is the
(total) interest
•
The
$20
amount is the
simple interest
•
The
$1
amount is the
compound interest,
or
the interest on the interest
•
The
$121
amount is the
future value
FIN 300 - TVM Lump Sum
5

Lump-Sum Formula
•
A more general formulation…
𝑃𝑃
1 +
𝑖
𝑛
=
𝐹𝑃
•
PV is the Present Value (think of this as the
beginning amount)
•
FV is the Future Value (think of this as the
ending amount)
•
i = interest rate (or, return) per period
•
n = number of periods over which the
investment takes place
FIN 300 - TVM Lump Sum
6

Lump-Sum Formula
•
We call this a “lump-sum” problem because
no other money flows in to or out of the
account, either after the initial investment or
before we calculate the ending balance in the
account – in other words, one single lump-
sum is invested and stays put (is re-invested)
in the account until the end
FIN 300 - TVM Lump Sum
7

Compound Interest Example
•
Back to our previous example
•
Plug into the formula…
𝑃𝑃
1 +
𝑖
𝑛
=
𝐹𝑃
$100
1 + 0.1
2
= $121
or
$100(1.1)(1.1) = $110(1.1) = $121
FIN 300 - TVM Lump Sum
8

Compounding
•
We are
moving forward in time
, so we refer
to this as
compounding
FIN 300 - TVM Lump Sum
9
T=0
T=1
T=2
Invest
$100
(negative
cash-
flow)
Cash Out
$121
(positive
cash-flow)
Compounding
Forward in Time