A Future Financial Security Matter; What Is an Annuity Factor?
The circulation of working world nowadays goes rapidly, we are sued to work harder and harder and due to that we often forget about our plan in the future related to financial security. We do need a strong financial security in the future like an annuity. Annuity is usually provided by the company we are currently working on and is prepared in our first working day. There is a factor in an annuity, which influences the payment value and the whole system in an annuity. This factor is called Annuity Factor.
What Is an Annuity Factor? An annuity is a financial instrument that pays income in a series of regular payments in return for an initial capital investment. The payments accumulate interest up until the time they are paid out. An annuity factor is the present value of an income stream that generates one dollar of income each period for a specified number of periods. The annuity factor can therefore be multiplied by the periodic annuity payment to determine the present value of the remaining annuity payments.
Present Value of an Annuity
The present value of an annuity is the value of all future payments at the current time, or before they have earned interest for the investor receiving the payments. Therefore, to determine the present value of future payments, the interest they have earned by the time of their scheduled payout has to be backed out. Payments earn interest up until the time they are paid out. For example, the first future payment’s present value is P/(1+i), if P is the payout amount and i is the interest accumulated in one time period. If the interest is compounded, then the present value of the second future payment is P/(1+i)^2.
Present Value Formula
The present value formula is the core formula for the time value of money; each of the other formula is derived from this formula.
PV = P/(1+i) + P/(1+i)^2 + P/(1+i)^3 + P/(1+i)^4 + … + P/(1+i)^n
can now be rewritten as:
P/(1+i) * [ 1 + P/(1+i) + P/(1+i)^2 + P/(1+i)^3 + P/(1+i)^4 + … + P/(1+i)^(n-1) ] (to make the first term 1; notice the change to n-1)
P/(1+i) * [1 – 1/(1+i)^n] / [1- 1/(1+i)]
Multiplying through the denominator of P gives
P * [1 – 1/(1+i)^n] / i
Note that this formula is not applicable if i=0, but then if i=0 in the first place, solving for PV was trivial.