The annuity is a series of periodic payments for a defined period of time. For many payments, the recipient can opt for a lump-sum payment or an annuity payment depending on their requirement since each option has its advantages and disadvantages. There is a possibility that the lump sum may be lost due to fraud or other reasons. Many people prefer to receive the annuity payment if they are using it for paying their expenses since the payment is periodic like many of the expenses. While choosing the annuity payment option, they will like to find out the value of the payment in the future, so that they can plan their finances accordingly.

**Definition**

**The future value of annuity continuous compounding, is the value of the annuity payment at a specified time in the future, with the annuity amount being compounded continuously.** The future value is used to calculate the ending balance of the annuity payments at the end of the period over which the payments have to be made. It indicates the value of the cash flow resulting from the annuity payment at a future date if continuous compounding is considered. The future value is higher than the present value and indicates the returns on the investment for the investor making the initial payment.

Formula

The future value of a particular annuity with continuous compounding, abbreviated at FVA, is calculated using the following annuity formula continuous compounding formula:

FVA = CF X ( (e^rt – 1)/(e^ r – 1))

where CF = cash flow from the annuity

r = interest rate

t = time period

Cash flow is the sum of each of the periodic payments for the annuity, the cash which will be paid out.

It should be noted that continuous compounding differs from periodic compounding, where the period for compounding is specified. In continuous compounding, the compounding is taking place continuously at every moment, hence the formula will differ. The returns from continuous compounding are usually more than the returns from periodic compounding since the compounding frequency is higher.

**Explanation**

For understanding the future value of the annuity when continuous compounding, the investor should understand the concepts of the future value as well as the continuous compounding. Since the annuity consists of a number of payments regularly, the future value will be the sum of each of these payments. The interest is added to each payment and the total amount will be compounded. Continuous compounding is constantly taking place, it is fluid and the principal amount will be compounded at all times, so the formula for continuous compounding is different from that of periodic compounding

Typically the formula for calculating the amount after continuous compounding = P e ^rt

where P is the original principal amount, r is the interest rate, t is the time period

This concept of future value is important for investors who wish to choose between the various investment options, and wish to select a low-risk investment with good returns. If the bank or other organization is offering an annuity with continuous compounding, they would like to compare with the other options which are available and make a decision.