19.a.
Interest, Present and Future Value, and Investment Decisions
Future Value and Present Value
Interest is generally defined as the price paid for borrowing and lending money and it is expressed as a percentage
rate over a specified period of time. The rate of interest, represented by the term R, can be used to calculate the
present value of future payments, as well as the future value of money invested today.
Present value (PV), also
called the bond price, can most easily be defined as the current value of a future cash payments, discounted at a
specific interest rate.
Future value (FV), on the other hand, is simply the value of a present amount of money at
some specified time and interest rate in the future.
When a person buys bonds, he or she is lending money and when
a person writes and sells bonds, he or she is borrowing money.
The seller of the bond agrees to repay the principal
amount at a specified time along with interest to the buyer of that bond.
Below are the basic calculations of PV and FV for four different situations: one period, multiple periods,
perpetuities, and annuities, along with some example problems.
I.
One Period
A.
A________
→
_______
A (1+R)
FV = A (1+R)
0
1
Ex: You put $100 in the bank for one year at an interest rate of 10%.
How much is it worth after one year? It is
worth: FV = 100 (1+.10) = $110
B.
B/(1+R)____
←
__
B
PV = B/(1+R)
0
1
Ex: A bond promises to pay $110 in one year at an interest rate of 10%.
How much is it worth today?
Today it is
worth: PV =110/(1 +.10) = $100
II.
Multiple Periods – “n periods”
A.
A
→
A(1+R)
→
A(1+R)
2
→
A(1+R)
n
FV = A(1+R)
n
0
1
2
n
Ex: You put $100 in the bank at an interest rate of 10%.
How much is it worth after 3 years?
It is worth:
FV = 100(1.10)
3
= $133
B.
B/(1+R)
n
←
B/(1+R)
2
←
B(1+R)
←
B
PV = B/(1+R)
n
0
1
2
n
Ex: I owe you $133 in three years, with an interest rate of 10%.
What is the bond price?
The bond price is: PV =
133/(1.10)
3
= $100
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I.
Perpetuity
(a constant stream of identical cash flows without end)
A.
B/R
←
B
←
B
←
B
PV = B/R
0
1
2
∞
Ex: The holder of a bond receives a payment of $5 per year forever and the interest rate is 5%.
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 Summer '98
 Baim
 Interest Rates, Time Value Of Money

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