The Formula of Mathematical Financial Annuities

Definition of Annuity

An annuity is an amount of loan repayment of an equal amount paid out over a period of time, and consists of the interest and the installment.

Annuity formula:

Annuity = Installment + Interest

AN = A_n + B_n

Formula Installment:

A_n = A₁ (1 + i) ^n-1

Information :

AN = Annuity

A_n = nth installment

A₁ = 1st installment

i = Interest Rate

B_n = The nth interest

Example:

A Loan will be repaid with a monthly annuity system. If the annuity amount is $.400.000,00. Please determine the 5th installment if the 5th Interest $.315.000,00 !!!!

Answer:

AN = $400,000

B₅ = $315,000
AN = A₅ + B₅
$400,000 = A₅ + $315,000
A₅ = $400,000 - $315,000
A₅ = $85,000

So the 5th installment is $85,000