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Basic Math and Statistics for Finance and Investment

Following equations are partially applicable for the benefit of your Trading and Investment but not compulsory. Normally these equations are quite basic for solving many finance and investment problems in real world sense. “Introductory Statistics” and “Time value of Money” parts should be understood by all traders and investors before they trade on real live trading. It is our recommendation even though many traders skip these parts.

1. Introductory Statistics

N = number of observation

Mean,

Population variance,

Population standard deviation,

Population Covariance =

Sample variance,

Sample standard deviation,

Sample covariance =

Correlation Coefficient, r =   using sample covariance.

2. Time Value of Money

Rate of return (ROR)

Rate of return,
Where

C1 = realization of investment at the end of the year
C0 = investment at the beginning of the year

Future value of a single sum

Future value,

Where

PV = principal or present value of a single sum
r = interest rate
n = number of compounding periods

Present value of a single sum

Present value,

Where

FV = future value or cash flow at the end of period n
r = discount rate
n = number of compounding periods

Future value of a series of cash flows

Future value,

Where

Ct = Cash flow at the end of period n
r   = interest rate
n  = number of compounding periods

Present value of a series of cash flows
Present value,

Where

Ct = Cash flow the end of period n
r   = interest rate
n  = number of compounding periods

Net present value

Net present value,   if the capital outlay occurs only at the beginning of the project

Net present value,   if the capital outlay occurs in different years of the project

Where

CO = the capital outlays at the beginning of the project
COt = the capital outlays at end of period n
Ct = Cash flow the end of period n
r   = interest rate
n  = number of compounding periods

Present value of a perpetuity

Present value of a perpetuity,

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
r    = the compound interest rate per period

Internal rate of return (IRR)

The internal rate of return is the discount rate that makes net present value equal to zero.

Where

Cn = Cash flow the end of period n
IRR = internal rate of return
n = period

3. Compounding Interest basics

Amount in compound interest
Amount,   or
Where
i = r/k = interest rate per period
n = kt = total number of conversion periods

Where
r = nominal interest rate per year
k = number of conversion periods per year
t = number of years (or term)

Present value in compound interest

Amount in continuous interest

Amount,

Where
e = natural base = 2.718281828

Present value in continuous interest

Present value,

4. Effective Interest Rate

Annual percentage rate (= nominal annual interest rate)

Annual percentage rate,

Where
i = rate per compounding period
n = number of compound periods in a year

Effective annual interest rate in compound interest transaction

Effective annual interest rate,

Where

r = nominal (= simple) interest rate per year (= APR)
k = number of conversions per year

Effective annual interest rate in continuous interest transaction

Effective annual interest,

Where

r = nominal (=simple) interest rate per year (=APR)

5. Annuity Equations

Future value of an ordinary annuity

Future value of an ordinary annuity,
Where

P   = the cash flow received/paid under the annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of an ordinary annuity

Present value of an ordinary annuity,

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Periodic payment into a sinking fund (=future value)

Periodic payment,

Where

FV = the future value to meet
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Future value of an annuity due

Future value of an annuity due,

Where
P   = the cash flow received/paid under the annuity
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of an annuity due

Present value of an annuity due,
Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period

Present value of a deferred annuity

Present value of a deferred annuity,

P   = the cash flow received/paid under annuity (i.e. periodic payment)
n    = the number of cash flows that form the annuity
r    = the compound interest rate per period
x   = the number of period before the first cash flow

Present value of a perpetuity

Present value of a perpetuity,

Where

P   = the cash flow received/paid under annuity (i.e. periodic payment)
r    = the compound interest rate per period