Standard Deviation; Factorial; The Rent Or Buy Decision - HP 12c User Manual

192 Appendix D: Formulas Used
⎡
⎢
⎣
=
r
⎡
∑
2 −
⎢
x
⎢
⎣

Standard Deviation

∑
2
n x
=
s
x
n ( n

Factorial

0! = 1
For n > 1 where n is an integer:
n
∏
=
n ! i
=
i 1

The Rent or Buy Decision

Market Value = PRICE(1 + I)
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
File name: hp 12c_user's guide_English_HDPMBF12E44
Printered Date: 2005/7/29
∑ ∑
⋅
⎤
x y
∑
−
xy
⎥
n ⎦
( )
( )
⎤ ⎡
∑ ∑ 2
2
x y
∑
⋅ 2 −
⎥ ⎢
y
n n
⎥ ⎢
⎦ ⎣
( )
∑ 2 ∑
− 2
x n y
=
s
y
−
) 1 n ( n
n
Page: 192 of 209
Dimension: 14.8 cm x 21 cm
⎤
⎥
⎥
⎦
( )
∑ 2
−
y
−
) 1