How do I determine the current value of the annuity?

The present value of the annuity or the final current current of the same size is calculated by determining the discounted value of each payment and adding them together. This value takes into account the different times when payments are made - the payment made in the future has less than the same amount due to such factors as uncertainty and the costs of the opportunity. If you want to calculate it, divide the payment amount by 1 plus a discount rate for the first period; This is the current value of the first period. In the second period, earn the amount of payment by 1 plus discount rate for the first period multiplied by 1 plus discount rate for the second period; Repeat for each following period.

Calculating the present value of the annuity is provided by the formula: PV = C/(1+R _{1 )+C/[(1+R 1 ) (1+R (1+R t ). In the formula, the C is also called an annuity payment, also called coupon. The discount rate for each period is reprazentoVána r t and t is the number of periods.}

If the discount rate is constant throughout the time over which the annuity makes payments, you can use the formula PV = C/R*(1-1/(1+R) t

). This formula is derived from the method of calculating the current value of the annuity step by step. If the discount rate is always R, the current value of the first payment C/(1+R) is the current value. The current value of the second payment is C/(1 + R)^2 etc. The present value of the annuity is therefore represented: PV = C/(1 + R) + C/(1 + R) 2 + ... + C/(1 + R) T-1 + C/(1 + R)

The annuity can be considered shorter eternity. This means it would be an endless series if payments never stop. Annuity Ince is final, you must calculate the sum of the final series. You want to do this, calculate the sum of the endless series as if the payments continue forever, and then subtract the sum of the endless series that represents the paymenty that will never be done. The current value of the payments series after stopping the annuity is calculated with the formula: PV = C/(1+R)

The sum of the endless geometric series, in which the terms are described and (1/b) ^k

, where K differs from zero to infinity, is represented and/(1- (1/b)). For an annuity with a constant discount rate is and is C/(1+R) and B (1+R). The sum is c/r. For a number of payments that will never be made, and is C/(1+R) t+1 and B is (1+R). The sum is c/[r*(1+r)

t ]. The difference gives the current value of the annuity that is final: c/r*[1-1/(1+r) t ].

The formula for the current annuity value is used for calculations for fully amortizing loans or loans in which the final number of the same size pays interest and main. One example of a fully amortizing loan is the residential mortgage. Since payments are often made monthly while rates are annualized, you must adjust the numbers when you make calculationsa. Use the number of payments for T and Divide R by the number of payments per year. If the number of payments is uncertain, as in lifelong annience, then the mathematical data mathematical data will be used to estimate the number of payments that will be made, and this number is used to calculate the current value.