Annuity payment from future value is a formula that helps one to determine the value of cash flows in an annuity when the future value of the annuity is known. Put simply, when the future value amount is known, we can use the annuity payment from future value formula to calculate the value of each of the periodic cash flows that need to be made to generate the given future value amount in a specified number of years.

The annuity payment from future value formula is primarily used by investors to calculate the amount of savings they need to make periodically to achieve their targeted financial saving goals.

It is worth noting that this formula will be applicable only if the cash flow happens at the end of each period. If the cash flow happens at the beginning of each period, then we have to use the annuity due payment from future value formula instead.

## Annuity Payment from Future Value Formula

$$C = \dfrac{FV(r)}{(1+r)^{n} - 1}$$

- C = Value of each of the periodic cash flows made
- FV = Future value of the annuity
- n = number of payments made
- r = effective interest rate

The future value of the annuity is the cash amount that will be available at the end of the annuity period. The number of payments made during the annuity could be in years, months, or days.

The interest rate would be the effective rate at which the cash flows are expected to grow over the period of the annuity. This means that if the interest rate is provided in an annualized percentage rate (APR) basis, one has to divide the given APR with the number of times the payment is made in a year (compounding factor) to get the interest rate (r)

To illustrate, if the APR is 6% and cash flows happen every six months, then r will be equal to (APR/m)= 3% (6%/2) , where m is the compounding factor.

The above formula is derived from the future value of annuity formula which is:

$$FVA = C \times \bigg[\dfrac{(1 + r)^{n} - 1}{r}\bigg]$$

## Annuity Payment from Future Value Example

Anne is a 40-year-old investor who wants to retire by the age of 60. She wants to make sure that she has $1m in savings when she reaches the age of 60. On January 1^{st}, 2020, she decided to subscribe to a yearly annuity plan which provides an interest of 5% per year, the first payment for which was to be made only on December 31^{st}, 2020. Successive payments for the plan were to be made on December 31^{st} of the following years consecutively for the next 19 years.

How much money should she invest every year to achieve the targeted amount of one million dollars as of January 1^{st}, 2040?

Since Anne has to make the annuity payments only at the end of each year, we can use the annuity payment from future value formula to calculate the amount that Anne needs to invest every year to achieve one million dollars at the end of 20 years.

$$C = \dfrac{1000000(0.05)}{(1+0.05)^{20} - 1} - \$30{,}242.59$$

Therefore, Anne has to make a yearly payment of $30242.59 for 20 years to reach her savings goal of one million dollars as of January 1^{st}, 2040.

## Annuity Payment from Future Value Analysis

It is not uncommon for investors to get mixed up between the real-life applications of the formulas for annuity payment from future value and annuity payment from present value. The latter formula can be used only when the present value is known.

For instance, say you are taking a home mortgage loan for $500,000 for 10 years and you need to calculate how much you need to pay per instalment (Equated Monthly Installment), then you will need to use the annuity payment from present value formula. This is because the loan amount of $500,000 happens to be the present value of the loan while the future value of this loan amount (after 10 years) is still unknown.

Also, note that the present value (the loan amount in this case) will steadily decrease after the payment of each instalment.

On the other hand, if you want to save up $10,000 in three years, then you can use the annuity payment from future value formula to calculate the amount of money that you would need to save up periodically since the targeted amount of $10000 is the future value of the annuity and not the present value. In this case, the balance keeps steadily increasing after each of the cash flow payments.

So, as an investor, it is essential for you to identify your financial planning goal and accordingly apply the appropriate formula.

- If your goal is loan repayment and payments are made at the end of each period, use the formula for annuity payment from present value
- If your goal is loan repayment and payments are made at the beginning of each period, use the formula for annuity due payment from present value
- If the objective is to achieve a desired future savings goal and cash flows are made at the end of each period, use the formula for annuity payment from future value
- If the objective is to achieve a desired future savings goal and cash flows are made at the beginning of each period, use the formula for annuity due payment from future value

## Annuity Payment from Future Value Conclusion

To sum up:

- Annuity payment from future value helps one to calculate the value of cash flows when the future value is known
- It is primarily used by investors in estimating the amount of periodic cash flow payments to be made to achieve the desired nest egg for retirement
- This formula can be used when the cash flow payments are made at the end of each period
- Investors have to differentiate between their savings and loan repayment financial goals and apply the appropriate annuity payment formula in their financial planning calculations.

## Annuity Payment from Future Value Calculator

You can use the annuity payment from future value calculator below to quickly work out the calculate the value of each of the periodic cash flows by entering the required numbers.