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192 Appendix D: Formulas Used
File name: hp 12c_user's guide_English_HDPMBF12E44 Page: 192 of 209
Printered Date: 2005/7/29 Dimension: 14.8 cm x 21 cm
()
()
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−⋅
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
−
⎥
⎦
⎤
⎢
⎣
⎡
⋅
−
=
∑
∑
∑
∑
∑
∑
∑
n
y
y
n
x
x
n
yx
xy
r
2
2
2
2
Standard Deviation
()
)1(
2
2
−
−
=
∑∑
nn
xxn
s
x
()
)1(
2
2
−
−
=
∑∑
nn
yyn
s
y
Factorial
0! = 1
For n > 1 where n is an integer:
∏
=
=
n
i
in
1
!
The Rent or Buy Decision
Market Value = PRICE(1 + I)
n
where:
I = appreciation per year (as decimal)
n = number of years
Net Cash Proceeds on Resale = Market Value – Mortgage Balance – Commission
The interest rate is obtained by solving the financial (compound interest) equation
for i using:
n = number of years house is owned
PV = down payment + closing costs
PMT
= mortgage payment + taxes + maintenance
–
rent – (% tax)
(interest + taxes)
FV = net cash proceeds on resale
Annual interest rate = 12 × i