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ANALYSIS OF THE CROATIAN PENSIONER’S DOUBT 2005th
Drago Francisković
; Međimurje University of Applied Sciences, Čakovec, Croatia
Sažetak
This paper answers the question that was, at the end of year 2005, set in front of the majority of Croatian pensioners. The government put forward a plan of debt repayment to each pensioner, giving him/her an
option of two models: A fast (accelerated) model and a regular model of debt repayment. The paper analyzes and compares these two models, depending on the pensioner’s age, gender and individual rate of value of money i . The paper presents mathematical expressions for calculating the present value of all payments for both models. The model with greater present value is considered to be better option for a person at age x . The goal is to find a critical (turning) rate xi ~ at which the profitability of both models equalizes. Analysis of the conditions of existence and uniqueness of rate xi ~ is done for any age x . Finally, for women, men and total population, turning point curve in the x-i plane is shown. Coordinates of the turning points (x,~ix ) , are
crucial values for which the present value of both models have the same amount, i.e. where the profitability goes from one to another model. In other words, the critical value of rate xi ~ , for each pensioner at age x with his/her own individual rate of value of money i , was found. If i ~ix the better choice is the fast model, otherwise if i ~ix the better choice is the regular model.
Ključne riječi
actuarial model; retiree; pensioner’s debt repayment; debt service models; Descartes' rule of signs; turning point curve; critical rate
Hrčak ID:
96621
URI
Datum izdavanja:
28.2.2011.
Posjeta: 1.210 *