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How did the formula of annuity cost change from residual income multiplied by present value coefficient to residual income multiplied by discount rate, and how did this formula change?
Since the present value coefficient of annuity =( 1- compound interest present value coefficient)/discount rate, we can know that the present value coefficient of compound interest = 1- annuity present value coefficient × discount rate. Replace the present value coefficient of compound interest to get the following formula.

Annuity cost = (original investment-residual income * compound interest present value coefficient+plus "annual operating cost present value")/annuity present value coefficient

= (original investment-residual income+residual income-residual income * compound interest present value coefficient+"annual operating cost present value")/annuity present value coefficient

= (original investment-residual value)/annuity present value coefficient+residual income *( 1- compound interest present value coefficient)/annuity present value coefficient+

Plus "annual operating cost present value"/annuity present value coefficient

= (original investment-residual value)/annuity present value coefficient+residual income * [1-1(1+I) n]/{[1-(1+I)-n]/I.

Add the "annual operating cost present value"/annuity present value coefficient, and the following formula can be obtained.

= (original investment-residual value)/annuity present value coefficient+residual income *i+∑ (annual operating cost present value)/annuity present value coefficient.

Extended data

In the annuity cost formula, the calculation and deduction of residual income are as follows

Since the present value coefficient of annuity = [(1-(1+i) (-n)]/i and the present value coefficient of compound interest = (1+I) (-n), the present value coefficient of annuity =( 1- present value coefficient of compound interest)/

Annuity cost = residual income ×( 1- annuity present value coefficient× discount rate)/annuity present value coefficient

Molecular multiplication:

= (residual income-residual income × present value coefficient of annuity × discount rate)/present value coefficient of annuity

Remove the brackets and become two items:

= residual income/annuity present value coefficient-residual income × discount rate

Associated with the previous negative sign, it is-residual income/annuity present value coefficient+residual income × discount rate.

Baidu encyclopedia-annual cost comparison method

Baidu Encyclopedia-present value coefficient of annuity