1
Finance  I
(MGCR 341)
– Prof. de Mot a
INTEREST RATES
2
Finance  I
(MGCR 341)
– Prof. de Mot a
Required Reading
•
Chapter 5
, “
Interest Rates
” from Berk and De Marzo
,
Corporate Finance
.
3
Finance  I
(MGCR 341)
– Prof. de Mot a
Question
Mary takes a $1 twoyear loan at a 2year interest of
10%. What is the interest rate that Mary pays per year?
Answer
 After two years Mary has to pay:
 The equivalent annual interest rate is:
 Notice that:
1
.
1
$
1
1
.
1
=
×
%
88
.
4
1
.
1
$
1
)
1
(
2
=
⇒
=
×
+
r
r
()
2
/
1
2
1
.
0
1
0488
.
0
1
1
.
0
1
)
0488
.
0
1
(
+
=
+
⇒
+
=
+
4
Finance  I
(MGCR 341)
– Prof. de Mot a
Question
Mary takes a $1 twoyear loan at a interest of 5% per
year. What is the interest rate that Mary pays over the
twoyear period?
Answer
 After two years Mary has to pay:
 Hence the interest rate over the twoyear period is:
 Notice that:
1025
.
1
$
1
*
)
05
.
1
)(
05
.
1
(
=
%
25
.
10
1
1
1025
.
1
Rate
Year
2
=
−
=
−
1025
.
0
1
)
05
.
1
)(
05
.
1
(
+
=
5
Finance  I
(MGCR 341)
– Prof. de Mot a
Adjusting the Discount Rate
to Different Periods
%
02
.
44
1
1)
0.00
(1
Rate
Discount
nnual
Equivalent
365
=
−
+
=
A
1
r)
(1
Rate
Discount
Period

Equivalent
n
−
+
=
n
%
54
.
9
1
0.2)
(1
Rate
Discount
nnual
Equivalent
0.5
=
−
+
=
A
Example
1. Quoted Rate:
0.1% per day
2. Quoted Rate:
20%
per a twoyear period
%
31
.
2
1
0.2)
(1
Rate
Discount
Quarterly
Equivalent
8
1
=
−
+
=
6
Finance  I
(MGCR 341)
– Prof. de Mot a
If a bank pays 24% over a sixyear period,
what is the effective annual rate?
a.
3.65%
b.
4.00%
c.
90.66%
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2
7
Finance  I
(MGCR 341)
– Prof. de Mot a
If a bank pays 24% over a sixyear period,
what is the effective annual rate?
%
65
.
3
1
0.24)
(1
Rate
Anual
Equivalent
6
1
=
−
+
=
8
Finance  I
(MGCR 341)
– Prof. de Mot a
Problem
Your bank account pays interests monthly with an effective
annual rate of 6%.
Part a.
What interest rate will you earn each month?
%
4868
.
0
1
0.06)
(1
Rate
onthly
Equivalent
12
1
=
−
+
=
M
9
Finance  I
(MGCR 341)
– Prof. de Mot a
Problem
(cont)
Part b.
If you have no money in the bank now, how much will
you need to save at the end of each month to accumulate
$100,000 in 10 years?
The proposed cash flow stream is a 120 period annuity (i.e.,
10 years x 12 months) with and interest rate
of 0,4868% per
period (i.e., per month) and a future value of $100,000. The
problem asks for the constant payment C of this annuity.
Using the future value of annuity formula and solving for C:
[]
month
per
47
.
615
$
1
)
004868
.
0
1
(
004868
.
0
1
000
,
100
1
)
1
(
1
120
=
−
+
=
−
+
=
n
n
r
r
FV
C
10
Finance  I
(MGCR 341)
– Prof. de Mot a
What is the present value on a lottery prize that is to
be received in 40 equal semiannual
payments of
$125,000, with the first payment beginning in one
year
? Assume an EAR
of 7%.
a.
1,666,463
b.
2,604,454
c.
2,694,047
11
Finance  I
(MGCR 341)
– Prof. de Mot a
What is the present value on a lottery prize that is to
be received in 40 equal semiannual payments of
$125,000, with the first payment beginning in one
year? Assume an EAR of 7%.
Solution
Effective SixMonth Rate
()
3.44%
1
07
.
0
1
5
.
0
=
−
+
=
454
,
604
,
2
)
0344
.
0
1
(
1
1
0344
.
0
000
,
125
0344
.
0
1
1
40
=
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
−
+
=
PV
12
Finance  I
(MGCR 341)
– Prof. de Mot a
Annual Percentage Rate (APR)
Annual Percentage Rate (APR):
The rate that you
would
receive over one year if your investment earned a simple
interest rather than compounded interest.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 trainor
 Annual Percentage Rate, Debt, Prof. de Motta

Click to edit the document details