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Test3A_Winter2016.docx
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Test3A Winter2016.docxName ...
Test3A_Winter2016.docxName_______________________________________ Perm #_______________________________ Econ 134A John
Test3A Winter2016.docxName ...
Test3A_Winter2016.docxName_______________________________________ Perm #_______________________________ Econ 134A John
Page 12
17. (7 points) Kaja is about to buy her first house. She will pay $600,000 for the house, 30% in cash and the
rest will be covered by a 50year mortgage. As part of the terms of the mortgage, Kaja will make payments
of $100,000 18½ years, 28½ years, and 38½ years from today. She will also make 50 equal
yearly
payments
of $
N
, starting one year from today. The stated annual interest rate of the mortgage is 15%, compounded
monthly. How much does
N
need to be in order to exactly pay off the mortgage?
Page 13
NOTE: YOU CAN TEAR THIS SHEET OFF
AND USE AS EXTRA SCRATCH PAPER.
PLEASE NOTE THAT ANYTHING ON THIS
SHEET WILL NOT BE GRADED UNLESS
EXPLICITLY SPECIFIED ON THE TEST.
Perpetuity
PV
=
C
r
Annuity
PV
=
C
r
[
1
−
1
(
1
+
r
)
T
]
Growing perpetuity
PV
=
C
r
−
g
Growing annuity
PV
=
C
[
1
r
−
g
−
1
r
−
g
×
(
1
+
g
1
+
r
)
T
]
Quadratic formula
ax
2
+
bx
+
c
= 0
è
Logarithmic rule
a
b
=
c
è
b = log c / log a
Variance of a sample
Var
=
1
T
−
1
∑
i
=
1
T
(
R
i
−
¯
R
)
2
Variance of a distribution, with each outcome
having the same probability of occurring
Var
=
1
T
∑
i
=
1
T
(
R
i
−
¯
R
)
2
Covariance formula
σ
X,Y
=
Cov
(
X
.
Y
)=
∑
i
=
1
N
(
x
i
−
¯
x
)(
y
i
−
¯
y
)
N
Correlation of A and B
Corr
(
A,B
)=
Cov
(
A,B
)
SD
(
A
)×
SD
(
B
)
, where SD stands
for standard deviation
Variance of a portfolio
X
A
2
σ
A
2
+
2
X
A
X
B
σ
A,B
+
X
B
2
σ
B
2
x
=
−
b
±
√
b
2
−
4
ac
2
a
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