1
Interest Rates and Rates of Return
A key problem in financial markets is to make instruments with different payment
streams comparable. We do this via:
Present Value Analysis
: Comparing interest and principal directly in different periods is
not appropriate because timing matters. $1 today is generally not the same as $1
tomorrow.
x
If we know the interest rate
i
, then the
present value
of $1 received
n
periods in the
future is
PV of $1 = $1/(1+i)
n
Remark
: This shows immediately that bond prices and yield to maturity are
inversely
related. Discounting future payments at a higher rate reduces the present value of the
bond’s future payments and therefore reduces the price of the bond today.
x
If we know the price and future payment schedule but not the interest rate, then we
use the
yield to maturity
to calculate the interest rate for different credit instruments.
The yield to maturity (i.e., current yield) is the interest rate
i
that equates the PV of a
debt instrument with its current market value (i.e., price today).
There are four main types of loans that are explained below.
1.
Simple Loans
:
The borrower receives from the lender an amount called
principal
(P),
and agrees to pay the principal plus an additional amount called
interest
(i), at a given
maturity date.
Example
: Consider a 1year simple loan with 10% interest. Repayment after 1 year is:
Total Payment = P + iP = P(1+i)
$11,000 = $10,000 + (0.10)($10,000)
Solving for i, the yield to maturity is:
i = [$11,000  $10,000]/$10,000 = 10%
Note: For a simple loan, the yield to maturity is the same as the simple interest rate.
2.
Discount Bond
:
The borrower repays a specific
face value
(F) at maturity and
receives a smaller price (D) initially known as the
discount
.
Example
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 Spring '11
 Other
 Interest Rates

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