Present worth of an annuity

The present worth of an annuity, P, is the amount of money at the present time that if invested at a compound interest rate will yield the amount of the annuity, F, at a future time. This is useful for determining the periodic payments that can be made over a specified number of years in the future from an annuity. 

Annuity equations relating F and the periodic payments. A, are converted to equations relating P to A by combining them with Eq. (17.12) for discrete interest or Eq. (17.20) for continuous interest. This is often referred to as discounting the amount of the annuity to determine its present worth. In Table 17.7, under periodic interest, the discrete uniform-series sinking-fund deposit factor becomes the discrete uniform-series capital-recovery facte in the following manner  

Similarly, the continuous uniform-series capital-recovery factor with payments. A, at the end of each year is obtained  

When comparing two annuities involving many payments into the future, it can be very helpful to discount all of the payments to their present worth. This gives the principal required at the current time, invested at the current interest rate, to enable the payments to be made at the end of each annuity period. While the annuity is making payments, interest continues to be paid on the remaining balance. At the end of the term of the annuity, the balance is zero. 

Upon retirement at the age of 65, an employee has a retirement fund of 1,000,000. If this fund is invested at 8% compounded quarterly, how much can be paid to the retiree at the end of each month, if the fund is to diminish to zero at the end of 20 yr when the retiree would be 85  

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The present worth of an annuity is defined as the principal which would have to be invested at the present time at compound interest rate i to yield a total amount at the end of the annuity term equal to the amount of the annuity. Let P represent the present worth of an ordinary annuity. Combining Eq. (5) with Eq. (21) gives, for the case of discrete interest compounding,... 

Present worth of an annuity, 228 definition of 225-226 factors for, 223n., 236-237 method for determining depreciation, 285... 

The key to performing any economic analysis is the ability to evaluate and conpare equivalent investments. In order to understand that the equations presented in Table 9.1 provide a comparison of alternatives, it is suggested to replace the equal sign with the words is equivalent to. As an example, consider the equation given for the value of an annuity. A, needed to provide a specific future worth, F. From Table 9.1. Equation (9JT) can be expressed as... 

Discount factors represent sinple ratios and can be multiplied or divided by each other to give additional discount factors. For exanple, assume that we need to know the present worth, P, of an aimuity, A—that is, the discount factor for P/A— but do not have the needed equatiom The only available formula containing the annuity term. A, is the one for F/A derived above. We can eliminate the future value, F, and introduce the present value, P, by multiplying by the ratio of P/F, from Equation 9.6. 

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