# Future Value of Annuity Formula

• Investment contracts known as annuities are offered by financial institutions like banks and insurance companies. The issuer invests your money when you buy an annuity in order to generate income.

• The contract between the parties transfers risk from the individual to the insurer or annuity issuer. The discount rate, which is how annuity issuers make money, is a portion of the investment income that they keep.

• The income the annuity issuer earns, however, declines with each payment made to you. The sum of the cash payments made to you and the total income reduction the issuer experiences as the payments are made represents the total cost of the issuer making the annuity payments. To determine how to schedule payments and how much of their share (the discount rate) must be paid out in order to cover costs and turn a profit, issuers compute the future value of annuities.

## Formula

The future value of a regular annuity is calculated using the formula F = P * ([1 + I]N – 1)/I, where P is the payment amount. I is equivalent to the discount (interest) rate. N is the total number of payments; the “” denotes that N is an exponent. F represents the annuity’s projected value.

Calculating Future Annuity Value

Depending on the type of annuity, the formula for calculating the future value varies a little. At the end of every time period, regular annuities are paid. Annuities due are payments made at the beginning of each period. Every year, many annuities are paid. On the other hand, some annuities pay out on a semiannual, quarterly, or monthly basis.

1. An ordinary annuity that is paid once a year serves as the basis for the fundamental equation for calculating an annuity’s future value. The ordinary annuity formula, according to Trusted Choice, is F = P * ([1 + I]N – 1)/I.

2. The payment amount is P. The interest (discount) rate is the same as I. The number of payments is N (the “” denotes that N is an exponent).

3.  F stands for the annuity’s future value. For instance, if the annuity pays \$500 per year for ten years and the discount rate is 6%, you would have \$500 * ([1 + 0.06]10 – 1%/0.6) instead of \$500.

4.  The calculated future value is \$6,590.40. Accordingly, the total cost to the issuer over the course of ten years will be \$6,590.40 (\$5,000 in payments plus \$1,590.40 in interest that was not earned).

## How is the Future Annuity Due Formula Derived?

The value of a sum of money that will be paid on a specific date in the future is known as its future value. A series of payments made at the start of every period in the series constitute an annuity due. As a result, the formula for the future value of an annuity due refers to the value of a series of periodic payments, each of which is made at the start of a period, on a particular future date. Payments made to the pension plan beneficiary frequently have a stream of payments like this. The cash flows related to their products are calculated by financial institutions.

The following formula can be used to determine the future value of an annuity due (where a number of equal payments are made at the start of numerous consecutive periods):

P = (PMT [((1 + r)n – 1) / r])(1 + r)

Where:

• P is the estimated value of the upcoming annuity stream.

• PMT stands for the total of all annuity payments.

• R stands for interest rate.

• n is the quantity of time that payments must be spread out over.

• Taking into account a specific amount of compounded interest earnings that gradually accumulate over the measurement period, this value represents the sum that a stream of future payments will grow to. With the exception of adding an extra period to account for payments being made at the start of each period rather than the end, the calculation is the same as the one used to determine the future value of an ordinary annuity..

## Final Thoughts

The formula for calculating future value of annuity due calculates the value at a future time. In contrast to the present value for an annuity due, the future value of annuity due formula is used in situations where it is appropriate. Consider the scenario where a person or business wants to purchase an annuity from someone and the first payment is made today.

## An example of an annuity’s future value that is due

ABC Imports’ treasurer plans to put \$50,000 of the company’s money into a long-term investment vehicle at the start of every year for the following five years. He projects that the business will make 6% interest, compounded yearly. At the end of the five-year period, these payments should be worth the following:

P = (\$50,000 [((1 + .06)5 – 1) / .06])(1 + .06)

P = \$298,765.90

Another illustration would be if the investment’s interest accrued monthly as opposed to annually and the invested sum was \$4,000 at the end of each month. Here’s the calculation:

P = (\$4,000 [((1 + .005)60 – 1) / .06])(1 + .005)

P = \$280,475.50

One-twelfth of the full 6% annual interest rate is represented by the.005 interest rate used in the previous example.

## Calculation Methods (Step by Step)

The steps are listed below.

1. First, determine the payments that must be made during each period. Please keep in mind that the aforementioned formula only applies in the event of equal periodic payments. P stands for it.

2. The next step is to calculate the interest rate based on the current market rate. It represents the interest rate that the investor will earn on money invested in the market. Divide the annualized rate of interest by the number of periodic payments in a year to obtain the effective rate of interest. It is represented by the letter r, which stands for r = Annualized Rate of Interest / Number of Periodic Payments in a Year.

3. After that, the overall number of periods is determined by multiplying the annual number of periodic payments by the total number of years. It is represented by n, where n = Number of Years * Number of Periodic Payments in a Year.

4. Last but not least, as previously demonstrated, the future value of an annuity due is determined by periodic payments (step 1), the effective rate of interest (step 2), and the number of periods (step 3).

## FAQs

### Q1. How important is the future value of an annuity that is due?

Several situations call for the future value of an annuity due, such as: to figure out the life insurance premium. In the scenario where the monthly contribution serves as a periodic payment, provident fund calculations are made.

When assuming a specific rate of return, or discount rate, the future value of an annuity is the value of a collection of recurring payments at a specific point in the future. The future value of the annuity increases with the discount rate.

Simply put, the annuity is the future value of all the payments added together.

### Q2. Where does the future value of an annuity due?

Several situations call for the future value of an annuity due, such as: figuring out how much a life insurance premium will cost. When a monthly contribution serves as a periodic payment, the provident fund is calculated accordingly.

The amount of each annuity payment multiplied by the rate of interest into the number of periods minus one, which is divided by the rate of interest, and the sum is multiplied by one plus the rate of interest are the formulas for calculating future value of annuity due. Each payment is made at the beginning of each period.

### Q3. What relationship exists between the future value of an annuity and the discount rate?

Future value is converted to present value by using either a discount rate or the interest rate that would be earned if an investment were made. The difference between present value and future value is how much money you’d need to invest today in order to earn a certain amount in the future. Future value tells you how much an investment will be worth in the future.

### Q4. How to Calculate Present Value Using Discount Rate

The investment return rate that is used to calculate present value is called the discount rate. In other words, the discount rate would be the rate of return that would be forfeited if an investor decided to accept a future payment instead of a current payment. Given that it represents the anticipated rate of return you would experience if you had invested today’s money for a period of time, the discount rate that is selected for the present value calculation is highly arbitrary.

### Q5. Present Value vs. Future Value

The time value of money principle and the need for additional risk-based interest rates are best illustrated by a comparison of present value with future value (FV). Simply put, time has a way of making money today worth more than it will be tomorrow. Future value can refer to the cash inflows from investments made with today’s funds or the required payments to repay today’s borrowings in the future.

### Q7. What is an annuity due?

An annuity that is due immediately at the start of each period is known as annuity due. In contrast to an ordinary annuity, which pays out at the end of each period, an annuity due does not pay out. Rent, which is paid at the start of each month, is a typical illustration of an annuity due payment.

Depending on whether you are the payee or payer, you should consider whether a regular annuity or an annuity due is preferable. An annuity due is frequently preferred as a payee because you receive payment upfront for a predetermined period, enabling you to use the money right away and enjoying a higher present value than an ordinary annuity.

Since you make your payment at the end of the term rather than the beginning, an ordinary annuity may be more advantageous for you as the payer. You can use those funds for the entire time period without paying

You frequently don’t have a choice in what you are given. Insurance premium payments, for instance, are an example of an annuity due, with premium payments due at the start of the covered period. An ordinary annuity is one that has payments due at the conclusion of the covered period, like a car payment.

### Q8. What is the annuity due’s present value?

A series of cash flows from an annuity due that start right away are valued today as their present value, or present value of an annuity due. Each period’s opening is when the annuity payments are distributed. With a few exceptions, this is very similar to determining the present value of an annuity.

You should first have a firm grasp of what an annuity is and the two types in order to comprehend the present value of an annuity due. A series of payments made over a set period of time is known as an annuity.

The first type of annuity, an ordinary annuity, distributes payments at the conclusion of the pay period. As an alternative, payments on an annuity due are made at the start of the pay period. But how significant is this information? What impact will it have on the total amount of money invested?

It’s because an annuity’s results will be impacted by the time value of money. Due to the concept of the time value of money, an investment made today would be worth more than one made tomorrow. Since everything else is equal, an annuity due will always be worth more than a regular annuity. This makes understanding the distinctions between the formulas for calculating the present value of an annuity and an annuity due essential.