Loan with payments in geometric progression

Increasing instalments (amortization with instalments in geometric progression). In this modality, the calculation of instalments is increasing geometrically according to the percentage of increment established previously. The financing system has been used in the loans of officially protected housing and indicates a suitable financing system for projects in which the investment that has been financed generates increasing cash flows (see figure). The differences between the first and the last instalments in extended periods of time can be very high since the geometric progression is applied from the first instalment.

a1: Instalment of period 1.

C0: Borrowed capital.

n: Number of instalments payment periods.

q: Value of the progression (for a progression of t% it would be expressed as 1.0t)

i: Interest rate

The second instalment would be calculated with the formula a2 = a1 x 1.0t. The instalment n would be: an = an - 1 x 1.0t.

The geometric formula cannot be applied when the value q is greater than (1 + i) since, in that case, we obtain negative instalments.