Cheat Sheet 2 Math 141
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)
Simple Interest Formula0: A=P∗(1 + AP R ∗Y) Compound Interest Formula:A=P(1 + AP R
n)nY
Annual Percentage Yield: APY AP Y = (1 + AP R
n)n−1
Formula for Continuous Compounding:A=P∗eAP R∗Y
Savings Plan Formula: A=P M T ∗[(1+ APR
n)nY −1]
APR
n
Total and Annual Return: totalreturn =A−P
P
annualreturn =A
P(1/Y )−1
Current Yield of a Bond: current yield = annual interest payment
current price of bond
Loan Payment Formula: P M T =P∗
APR
n
»1−(1+ APR
n)(−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 m(joint) m(separate) head household
10% 1 - 7,550 1-15,100 1 - 7,550 1-10,750
15% 7,551 - 30,650 15,101 - 61,300 7,551 - 30,650 10,751 - 41,050
25% 30,651 - 74,200 61,301 - 123,700 30,651 - 61,850 41,051 - 106,000
28% 74,201 - 154,800 123,701 - 188,450 61,851 - 94,225 106,001 - 171,650
33% 154,801 - 336,550 188,451 - 336,550 94,226 - 168,275 171,651 - 336,550
35% 336,551+ 336,551+ 168,276+ 336,551+
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