Lily Qiu, Assistant Professor
Economics Department, Brown University
EC1710, Lecture 1516, spring 2010, page 1
Interest Rates and Bond Pricing
1. Present Value (PV) of Money:
To make our discussions simpler, for this part of our lectures, when we talk about
interest rates, we are assuming
annual
compounding unless specified.
a) If you will receive $7 next year, and the current interest rate is 40%, what is the value of this
future income as of today?
b) What is the formula?
r
C
PV
1
c) If you will receive that $7 in two years, and the current interest rate is 40% per year, what do
you value this $7 as of today?
PV =
d) What is the formula?
2
)
1
(
r
C
PV
The present value of cash C
t
received at time t is:
t
t
r
C
C
PV
)
1
(
0
Notation: here the interest rate is
constant
.
t
r
)
1
(
1
is called the
discount factor
 discounting the future cash flow to obtain the current
value/present value.
It is the PV of $1 received at time t.
2. Net Present Value
a) If you receive $1 in one year and another $1 in two years, and the prevailing interest rate is
40%, do you have the equivalent of $2 today?
b) What do you value this cashflow as of today?
PV =
c) If you need to pay $1 to get this cashflow, should you pay?
d) If the interest rate is 80% a year, should you pay?
NPV =
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View Full DocumentLily Qiu, Assistant Professor
Economics Department, Brown University
EC1710, Lecture 1516, spring 2010, page 2
The
Net Present Value
with infinite cashflows:
0
2
2
1
0
)
1
(
...
)
1
(
1
t
t
t
r
C
r
C
r
C
C
NPV
The first cash flow C
0
is often
negative,
i.e., the investment you initially put down in order to
receive all the future cash flows > thus the “net” in the name
3. Future Value of Money:
a) You invest $55,000 at an interest rate of 350 basis points above the 5% annual interest rate.
If the interest rate is annual compounded, what will you receive at the end of the year?
If the
interest rate is monthly compounded, and you reinvest monthly interest payments at the same
interest rate, what will you have at the end of the year?
4. Perpetuities
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 Spring '10
 Qiu
 Interest Rates, Time Value Of Money, Net Present Value, Assistant Professor Economics, Professor Economics Department

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