The current article describes the annuity loan scheme and exemplifies the calculation of the payment schedule for this scheme.

In the annuity scheme, a loan is repaid in equal monthly installments during a whole loan period. A total amount of a monthly installment (T) comprises a principal amount and interest amount. 

Calculating the monthly installment

The monthly installment is calculated by the following formula:

                    (1)

where

T - total amount of the monthly installment,

A - loan amount,

IR - monthly interest rate (hereinafter “the interest rate”),

NP - number of installments.

It should be noted that the interest rate in formula (1) is taken in hundredth. Therefore, the interest rate expressed as a percentage must be divided by 100. For example, the interest rate of 1% corresponds to IR = 0.01. 

Calculating the monthly interest and monthly principal

A repaid amount of the monthly installment covers the principal and interest. To split each monthly installment into these two payments, the system uses a recursive algorithm where each iteration corresponds to a next installment, i.e. a total number of iterations of the recursion equals NP. In each i-th iteration (each iteration corresponds to the i-th installment), the i-th interest amount and the i-th principal amount are calculated sequentially and the current balance is updated. Calculations are performed according to the following formulas:

                                   (2)

                                      (3)

                               (4)

where

I_i - interest amount of the i-th installment,

P_i  - principal amount of the i-th installment,

B_i - total outstanding principal amount (hereinafter “the balance”) at the moment of the i-th installment,

i - integer index that corresponds to an installment number in the payment schedule and takes on values from 1 to NP sequentially.

Formulas (2)-(4) are used sequentially for calculating corresponding values of the i-th installment (i = 1, 2, ..., NP). It should be noted that an initial balance corresponds to a loan amount, i.e. B₁ = A.

Thus, each month, different principal and interest amounts are repaid but the total amount of each monthly installment remains constant and equals T.

Example of the payment schedule calculated using the annuity scheme

Assume a loan is taken out in the amount of 1000 USD at the monthly interest rate of 1% for 3 months, i.e. A = 1000, IR = 0.01 and NP = 3.

Calculating the monthly installment