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MATH 034 Formulas

Simple Interest Formula I = PRT

I = simple interest

P = principal

R = simple interest rate

T= term

Nth Term of An Arithmetic Sequence an = a1 + (n – 1)d

a1 = first term

d = common difference

Sum of the First n Terms of an Arithmetic Sequence

Sn = (n/2)(a1 + an)

a1 = first term

an = nth term

Simple Discount Formula D = MdT

D = simple discount

M = maturity value

d = simple discount rate

T = term

Compound Interest Formula FV = PV(1 + i) n

FV = future value

PV = present value

i = interest rate per compounding period

n = number of compounding periods

N+1 st

Term of a Geometric Sequence an = a0 r n

a0 = first term

a1 = second term

r = common ratio = a1/a0

Sum of the First n Terms of a Geometric Sequence

Sn = a0 (1 – r n ) / (1 – r)

a0 = first term

r = common ratio = a1/a0

Infinite Geometric Sum

S∞ = a0 /(1 – r)

a0 = first term

r = common ratio = a1/a0

Compound Interest Rate

i = compound interest rate

FV = future value

PV = present value

n = number of compounding periods

Time Periods n = log (FV/PV)

log (1 + i)

i = compound interest rate

FV = future value

PV = present value

Rule of 72

The time required for a sum of money to double at

a compound interest rate of x% is approximately

72/x years. (x should not be converted to a decimal)

Rule of 72 (Alternate Form)

The compound interest rate required for a sum of money

to double in x years is approximately 72/x percent.

Effective Interest Rate Eff. Rate = (1 + r/c) c – 1

r = the nominal interest rate

c = the number of compoundings per year

Continuous Compounding FV = PV e (rt)

FV = future value

PV = present value

e = a mathematical constant (approx. 2.71828)

r = annual interest rate

t = number of years

Future Value Annuity Factor sn/i =

i = interest rate per payment period

n = number of payment periods

Future Value of an Ordinary Annuity FV = PMTsn/i FV = future value of the annuity

PMT = amount of each payment

sn/i = annuity factor

Future Value of an Annuity Due FV = PMTsn/i(1 + i)

FV = future value of the annuity

PMT = amount of each payment

i = interest rate per payment period

sn/i = annuity factor

Interest for Future Value Annuities

interest = FV – total deposits

Present Value Annuity Factor

i = interest rate per payment period

n = number of payment periods

Present Value of an Ordinary Annuity PV = PMTan/i

PV = present value of the annuity

PMT = amount of each payment

an/i = present value annuity factor

Present Value of an Annuity Due PV = PMTan/i(1 + i)

PV = present value of the annuity

PMT = amount of each payment

an/i = present value annuity factor

Interest for Present Value Annuities

interest = total deposits – PV

1/ ( ) 1

nFV i

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i

i a

n

in

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/

Sales Tax T = P(1 + r)

T = total price including tax

P = price before tax

r = sales tax rate

T – P = amount of tax

Income Tax Formulas

Annual taxable income

= annual income – benefits – exemptions – deductions

Paycheck taxable income

= paycheck income – benefits – exemptions

FICA taxes based on paycheck income – benefits

Dividends

dividend per share = total dividend

total # shares

individual dividend

= (dividend per share)(# individual shares)

current dividend yield = quarterly dividend per share × 4

market price per share

trailing divided yield = trailing dividend per share

market price per share

Compound Annual Growth Rate

or Rate of Return

i = compound growth rate

FV = future value

PV = present value

n = number of years

Net Asset Value (NAV)

NAV = total assets / total number of shares

Mutual Fund Shares

# shares = amount invested / NAV

Inflation Formula FV = PV(1 + i) n

FV = future value of an item

PV = present value of an item

i = rate of inflation

n = number of time periods

Declining Balance Depreciation FV = PV(1 + i) n

FV = future value

PV = present value

i = depreciation rate

n = years

Straight Line Depreciation

Total depreciation amount

= Original value – Residual value

Annual depreciation = Total depreciation amount

Useful Life

Depreciated value

= Original value – (# of years)(Annual depreciation)

Credit Card Interest I = PRT

I = interest

P = principal

R = interest rate

T= term

Mortgage Formulas

Equity = value of home – amount of mortgage

Total PITI = principal + interest + taxes + insurance(s)

One point = 1% of the amount of the loan

Payback period = cost of points / monthly savings

The 28% Rule

Total PITI cannot exceed 28% of gross monthly income.

The 36% Rule

Total PITI and all other long-term debt payments cannot

exceed 36% of gross monthly income.

Lease Payment = Payment on Loss +

Interest on Residual Payment on loss: Use PV = PMTan/i where

PV = original price – residual value

Interest on residual: Use I=PRT where P = residual value

Markup Based on Cost P = C(1 + r)

P = selling price

C = cost

r = percent markup

Markup Based on Selling Price C=SP(1 – r)

C = item’s cost

SP = selling price

r = gross profit margin

Markdown MP = OP(1 – d)

MP = marked-down price

OP = original price

d = percent markdown

Profit Margin Formulas

Gross profit = sales – cost

Gross profit margin = gross profit / sales

Gross profit = (gross profit margin)(sales)

Net profit = sales – cost – expenses

Net profit margin = net profit / sales

Cost-Revenue Analysis

P = R – C

P = profit function

R = revenue function

C= cost function

1/ ( ) 1

nFV i

PV  