# Definition of Growing Annuity

A growing annuity refers to a series of regular payments that increase in amount with each payment. For example, you may start a business that you expect to generate incomes that grow until you sell it. You may also buy an investment vehicle that pays you regularly after you make an initial investment.

## Payments

By definition, the amounts of the payments of a growing annuity go up with time. The first payment of a growing annuity is the lowest amount and the last payment is the highest amount you will receive from it. You usually get these payments regularly. The time between two payments varies depending on the annuity itself. For example, you may get the payments each week, each month or each year.

## Time Period

A growing annuity has a definite starting date and a definite end date. The payments start one period after the beginning of the start of the growing annuity. For example, if you buy an investment that pays you regularly each month, you will make the initial investment today and earn the first payment next month. You will then earn one payment every month until the last day of the term of the annuity.

## Rates

Two rates determine the amount of payments you get each payment period. The interest rate determines the amount of the payments for all types of annuities, even those in which the payments remain at the same level throughout the entire term of the annuity. The growth rate shows the amount by which each payment is higher than the previous payment. When making calculations for a growing annuity, these rates should match the time period between payments. For example, if you have annual growth and interest rates but get monthly payments, you have to divide the rates by 12 to get the monthly rates.

## Calculations

To calculate any of the various features of a growing annuity, plug the numbers into the following formula: PV = C [1/(r-g) - (1/(r-g))*((1+g)/(1+r))^t ]. In this formula, r stands for the interest rate, g represents growth rate and t represents the number of payments. C represents the amount of the initial payment and PV stands for the present value, which is the value of the entire series of payments at the beginning of the term.

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