Cheat Sheet 2 Math 141
Cheat Sheet 2
Let A = accumulated balance after Y years P = starting principal AP R = annual percentage rate (as a decimal) n = number of compounding periods per year Y = number of years (may be a fraction) P M T = regular payment (deposit) amount a = inflation rate (a decimal) i = interest rate (a decimal)
Math 141
Simple Interest Formula: Compound Interest Formula:
Annual Percentage Yield: APY
Continuous Compounding Formula:
A = P (1 + AP R Y )
A
=
P (1
+
AP n
R
)nY
AP Y
=
(1
+
AP n
R
)n
-
1
A = P eAP RY
Savings Plan Formula: Total and Annual Return:
Current Yield of a Bond:
A
=
PMT
[(1+
AP R n
)nY
-1]
AP R
n
totalreturn
=
A-P P
annualreturn =
A P
(1/Y ) - 1
current
yield
=
annual interest payment current price of bond
Loan Payment Formula:
AP R
PMT = P
n
( ) 1-
1+
AP n
R
(-nY )
The CPI Formula
= CP IX
CP IY
priceX priceY
The Present Value of a principal P, Y years into the future, r=APR, a=annual inflation:
A
=
P
[
1+r 1+a
]Y
Real Growth g:
g
=
r-a 1+a
Real Growth over Y years:
g(Y )
=
[1 +
r-a 1+a
]Y
-1
The Tax Table: single
10%
1 - 9,275
15% 9,276 - 37,650
25% 37,651 - 91,150
28% 91,151 - 190,150
33% 190,151 - 413,350
35% 413,351 - 415,050
39.6%
415,051 +
m(joint) 1-18,550 18,551 - 75,300 75,301 - 151,900 151,901 - 231,450 231,451 - 413,350 413,351 - 466,950 466,951 +
m(separate) 1 - 9,275
9,276 - 37,650 37,651 - 75,950 75,951 - 115 725 115,726 - 206,675 206,676 - 233,475
233,476 +
head household 1-13,250
13,251 - 50,400 50,401 - 130,150 130,151 - 210,800 210,801 - 413,350 413,351 - 441,000
441,001 +
The mean of x1, x2, ...xn is
?
=
. x1+x2+...+xn n
The variance s2 of x1, x2, ...xn is
s = . 2 (x1-?)2+(x2-?)2+...+(xn-?)2 n-1
The standard deviation s is the square root of the variance s2.
Quartiles of Normal Distributions: Q1 = mean - .67 s Q3 = mean + .67 s
The 68 - 95 - 99.7 Rule for normal distributions: 68% of the observations fall within 1 standard deviation of the mean. 95% of the observations fall within 2 standard deviations of the mean. 99.7% of the observations fall within 3 standard deviations of the mean.
Given data (x1, y1), (x2, y2), ... (xn, yn), with means ?x, ?y and standard deviations sx, sy. The correlation between variables x and y is
r
=
1 (n-1)sxsy
[(x1
-
?x)(y1
-
?y )
+
(x2
-
?x)(y2
-
?y )
+
...
+
(xn
-
?x)(yn
-
?y)] .
The least squares regression line is where
y = ax + b.
a=r
sy sx
and
b = ?y - a?x.
For a simple random sample of size n,
the sample proportion of successes is
p
=
count
of successes
n
in the
sample
The mean of the sampling distribution is p
and the standard deviation is
p(1-p) n
.
The 68 - 95 - 99.7 Rule applies here aswell.
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