ADONGO'S TARGET BALANCE EQUATIONS

ADONGO’S TARGET BALANCE EQUATIONS

Today I am most glad to continue from my previous Diary(or Weblog) titled, “Adongo’s Minimum Uncertainty Method”.

In life insurance and theory of employment, interest and money, cash is needed to satisfy the transactions motive, the need to pay benefits. The disbursement of cash includes the payment of wages and salaries, trade-debts, death benefits and retirement benefits. The cash inflows(or premium) must be synchronized, if not perfectly, nearly. The equality between the inflows(or premiums) and outflows(benefits) is to determine the company target-fund balance.

The target- fund balance involves a trade-off between the benefits of holding too much cash and premiums of holding too much benefits.

Consider a discrete whole life policy purchase each of the lx lifes for an annual premium. If l_x+k survive at years x+k and d_x+k death between x+k and x+k+1. At an effective annual rate of interest r, the net annual premiums  is;

NAP_x*lx+C_*NAP_x*l_x+1 +C²_*NAP_x*l_x+2 +...=Cd_x+C²d_x+1 +C³d_x+2 +......

Or

NAP_x +C_*NAP_x+C²_*NAP_x +....=C/q_x +C²/q_x+1 +C³/q_x+2 +.....

For each i=1,2,3,.....k

Where;

NAP_x=net annual premium at age x.

L_x+k=lifes purchase at age x+k.

C=Claims(or benefits)

d_x+k=death at age x+k.

FUND BALANCE

In Adongo’s(or my) target- balance equations, aggregate fund of balance to which benefits are withdrawn and which earns interest rate r, at the end of k^th year policy. The balance of the fund is;

B_f=∑l_x+kNAP_x - ∑_Cx+k

The net premiums are exactly sufficient to cover the benefits if only the balance of the fund at the end of the k^th year is zero(0).

REFERENCE

*Adongo's Ayine William(me), Diary(or weblog), "Adongo's Minimum Uncertainty Method"