# Growing Annuity Formula

The growing annuity formula is basically a total sum of future cash flow. Cash flow is increased by a certain rate gradually. The formula of growing annuity financial is This formula is basically used for the discounted future cash flows when jse 1 + g to factor. In this, you will see an increase in cash flow at an authentic rate.

You can also write the growing annuity formula by adding present values.

This can easily be said geometric series as (1+g)/(1+r) is said to be the simplest ratio. When you use geometric formula then the present value of the growing annuity will be

Later this specific formula can easily be simplified when you will multiply it by (1+r)/(1+r). This will surely cancel a lot of numbers by using this formula.

In the denominator, (1+r) – (1+g) will reverse as r-g. You will see P and r-g will be factored in. Later in the end you will get the present value of the growing annuity.

## Growing annuity formula Example:

The growing annuity due formula can easily be calculated by present-day value at a proportionate rate. It can be referred to as an increasing annuity as well. One of the simplest examples is that if a person receives \$150 in the first year and successive payments made increase 15% every year for a total of five years. This would be a recipient of any of these \$100, \$110, and \$121, respectively.

How to use a growing annuity calculator?

You can use the following calculator so you can easily figure out the present values of annuity, growing annuity, and perpetuity.

• Step 1: Period: It is denoted as a year but it can easily be used as a time interval.
• Step 2: Number of Periods (t): It is denoted as how many years
• Step 3: Perpetuity: For finding perpetuity it will approach infinity. You need to enter p, for perpetuity
• Step 4: Interest Rate (R): It is denoted as the annual nominal interest rate. r =R/100 which means the interest in the rate of the decimal.
• Step 5: Compounding (m): In this, you will see how many times there will be compounding per year. For instance, if a period is of a year then it means 1 and if it’s quarterly then it means 4, and if monthly then it will be 12, and if daily then 365 days.
• Step 6: Continuous Compounding: It occurs when the frequency of compounding increases to infinity. You have to enter c for continuous compounding.
• Step 7: Payment Amount (PMT): In this, you will find out the exact amount of the annuity payment every year.
• Step 8: Growth Rate (G): If you see that growing annuity is growing in a fast speed then you have to enter the growth rate per year for the payment calculated in percentage g = G/100
• Step 9: Payments per Period (Payment Frequency (q): You will check how often payment is made every year. If the period is for a year then you have to pay it annually and if it’s quarterly then for that you have to do it after every 4 months.
• Step 10: Payments at Period (Type): If you see the payment you have to check the arrears. Make sure all of them are zero.
• Step 11: Present Value (PV): In this, you have to calculate the value lump sum and payment of future cash flow.

## Growing Perpetuity Formula

Perpetuity formula actually denotes a flow of future cash. The values keep diminishing on and off. You need to keep growing the payment in order to get a higher rate. The current value of growing perpetuity is a bit difficult to calculate. The basic formula for growing perpetuity is as follow

D = Expected cash flow in period 1
R = Expected rate of return
G = Rate of growth of perpetuity payments

Make sure when you calculate G should always be greater than R. In case if it’s less in amount you won’t get an appropriate or authentic result.

Example:

As you see in universities there are certain funds which are used for different purposes. They require growing perpetuities. You will see that the expense list will increase gradually.

## Deferred growing annuity formula

This Deferred growing annuity formula is used for the calculation of present values of the deferred annuity. It is recovered after some time and is calculated by determining present values. All you need to make sure is to consider the rate of interest and period of time.

Here’s the deferred growing annuity formula

#### Deferred Annuity = P Ordinary * [1 – (1 + r)-n] / [(1 + r)t * r]

Here P ordinary is used for Ordinary annuity payment, r is used for an effective rate of interest, n is used for a number of periods, and t is used for deferred periods.

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## Future value of growing annuity formula The future value of a growing annuity can easily be calculated by checking out all the cash flows individually. When you check the growing and initial cash flow at g make sure its sufficient. Then find the future value of growing annuity formula excel of cash flow and the rate of interest. Then sum up all the values to find out the result.

The values can also be calculated by growing the present value of the growing annuity and the period. When you write the formula you have to write it like this.

This FV (GA) is shown as the future value of annuity while PV (GA) is the present of growing annuity. R is used as the periodic discount and n is used for the numbers of cash flow.

Try this out MACRS Depreciation Calculator

Example

Your parents plan to set a school fund for you so they can fund your 4 years program. The total tuition fees is \$40,000 per year which you have to pay in advance. The tuition fee might grow Upto 4% and the school fund will easily earn 8% interest per year. Now you have to calculate the total amount of school funds when you start your school.

For this you have to calculate the present values initially. Then there are 4 years so the growth rate will be 2% and in total there will be 8 semesters. For that you have to use the following equation.

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## How does the growing annuity Work?

All you need to do is place your values and apply the growing annuity formula in excel and all your values will be calculated instantly.

It can resolve complex calculations within seconds. Here is how you can easily use the increasing annuity formula. Y

ou need to enter the formula which is PV(RATE,NPER,PMT).

Rate is used to find out the discount rate. NPER is used to calculate the number of periods that are within the discount rate and PMT is used to calculate the amount of payment.

Example:

In case you are trying to find out the exact present value of the future annuity then the investment rate will be 5% for 12 years with calculated annual payment which will be calculated by the following formula which is =PV(.05,12,1000). Through this you will easily get the exact value of \$8,863.25.