Math formula and definitions

Interest - I

P × r × t

Future Value - FV

P(1 + rt)

Present Value - P

FV / (1 + rt)

Principal - P

I / rt

Rate - r

I / Pt

Rate - r (with future value)

[(FV / P) - 1] / t

Time - t

I / (Pr)

Time - t (with future value)

[(FV / P) - 1] / r

Amount - A

P(1 + r)^t

Compound Interest - I

A - P

Present Value - P

A / (1 + r)^t

Rate - r

ᵗ√(A/P) - 1

Time - t

log (A/P) / log (1+r)

Amount - A

P(1 + r/n)^(nt)

Present Value - P

A / (1 + r/n)^(nt)

Rate - r

Time - t

Future Value (Ordinary Annuity) - FV

Present Value (Ordinary Annuity) - P

Future Value (Annuity Due) - FVAD

Present Value (Annuity Due) - PAD

A

Amount (Future Value)

FV

Future Value

P

Principal / Present Value

I

Interest

Is

Simple Interest

R

Regular Payment (Annuity Payment)

r

Annual Interest Rate

i

Interest Rate per Period

n

Number of Compounding or Payment Periods

t

Time (Years)

Equal Payment

a fixed amount paid in every period of an annuity.

Payment Interval

the equal interval or period of time between successive payments.

Annuity Payment

the fixed payment made for each period of an annuity.

Types of Annuity

annuities may be classified according to the timing of payment, payment interval, and interest period.

Ordinary Annuity

an annuity where the payment is made at the end of each period.

Annuity Due

an annuity where the payment is made at the beginning of each period.

Simple Annuity

an annuity where the payment interval is the same as the interest period.

General Annuity

an annuity where the payment interval is not the same as the interest compounding period.

General Ordinary Annuity

a general annuity in which the periodic payment is made at the end of the payment interval.

Deferred Annuity

an annuity in which the periodic payment is not made at the beginning nor at the end of each payment interval, but some later date.

Perpetuity

a series of periodic payments which are to run infinitely or forever.

Future Value (Amount) of an Annuity (F)

the sum of the future values of all payments to be made during the entire term of the annuity.

Present Value of an Annuity (P)

the sum of the present values of all payments to be made during the entire term of the annuity.

Regular or Periodic Payment (R)

the amount of each payment.

Term of Annuity (t)

the time between the first payment interval and last payment interval.

Payment Interval

the time between successive payment dates of an annuity.

Interest Period

the time between successive conversions of interest.

Frequency of Conversion (m)

the number of conversion periods in one year.

Total Number of Conversion Periods (n)

the total number of conversion periods.

Nominal Rate (iₘ)

the annual rate of interest or interest rate per year.

Rate (j)

the interest rate for each conversion period.

Cash Value or Cash Price

the down payment (if there is any) plus the present value of the annuity.

Cash Flow

the movement of money payments and receipts represented in a time diagram.

Interest (I)

the amount paid or earned for the use of money.

Simple Interest (Is)

it is the interest that is computed on the principal and then added to it.

Compound Interest (Ic)

the interest is computed on the principal and the accumulated past interests.

Principal (P)

the amount of money borrowed or invested on the origin date.

Rate (r)

the annual rate, usually in percent, charged by the lender, or rate of increase of the investment.

Time or Term (t)

the amount of time in years the money is borrowed or invested, the length of time between the origin and maturity dates.

Maturity Value or Future Value (F)

the amount after t years that the lender receives from the borrower on the maturity date.

Origin or Loan Date

the date on which money is received by the borrower.

Maturity Date

the date on which the money borrowed, or loan is to be completely repaid.

Lender or Creditor

the person (or institution) that invests the money or makes the funds available.

Borrower or Debtor

the person (or institution) that owes the money or avails of the funds from the lender.

Actual Time

the actual number of days between two given dates.

Approximate Time

considers each month as having 30 days.

Present Value

the current value of a future amount of money.

Future Value

the value of an investment or amount of money at a specified future date based on a growth rate.

Compound Amount (A)

the principal amount plus the compound interest accumulated over time.

Frequency of Compounding

the number of times interest is added to the principal amount within a year.

Frequency of Conversion (m)

number of conversion period in one year.

Conversion or Interest Period

time between successive conversions of interest.

Total Number of Conversion Periods (n)

number of times interest is compounded.

Nominal Rate (iₘ)

annual rate of interest or interest rate per year.

Rate (j)

interest rate for each conversion period.

Maturity Value (Future Value) (F)

the amount received or paid at the end of the investment or loan period.

Simple Annuity

the payment interval is also the same as the interest period.

General Annuity

an annuity where the payment interval is not the same as the interest compounding period.

General Ordinary Annuity

a general annuity in which the periodic payment is made at the end of the payment interval.

Ordinary Annuity

an annuity where the payment is made at the end of each period.

Annuity

a sequence of payments made at equal (fixed) intervals or periods of time.

Payment Interval

the time between successive payments.

Deferred Annuity

an annuity in which the periodic payment is not made at the beginning nor at the end of each payment interval, but some later date.

Perpetuities

a series of periodic payments which are to run infinitely or forever.

Term of an Annuity (t)

time between the first payment interval and last payment interval.

Regular or Periodic Payment (R)

the amount of each payment.

Amount (Future Value) of an Annuity (F)

the sum of the future values of all payments to be made during the entire term of annuity.

Present Value of Annuity (P)

the sum of present values of all payments to be made during the entire term of annuity.

Cash Value or Cash Price

down payment (if there is any) plus present value of the annuity.

Periodic Payment

each payment in an annuity.