How to Calculate Immediate Annuity

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An annuity is a fixed amount of money invested to generate an income or payment stream. Annuities come in two types: immediate annuities and annuities due. Both types require an immediate investment, but an annuity due makes a payment to the holder immediately, at the beginning of the first payment period. On the other hand, an immediate annuity, also known as an ordinary annuity, because it's the most common type, begins paying at the end of the first payment period. Both types yield a cash flow of both principal and interest, over a pre-determined period, which you can use for retirement or other income. It's important to know how to calculate the payment stream if you want to know how much you'll receive each period from your immediate annuity.


Step 1

Determine how much money you have available to invest in your immediate annuity. This number will be represented by P for the immediate annuity initial payment or principle. For example, you may want to invest $50,000, so that in this case, P = 50,000.

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Step 2

Determine the rate of interest at which you can invest your money for the immediate annuity. Call this number "i," for the interest rate. Usually, interest rates are expressed annually, so if you want to receive your payments every month, divide i by 12 to get the correct interest rate. If the financial institution with which you invest offers an 8 percent rate of interest, i = .08000, and the monthly rate of interest is .08/12 = .006667.


Step 3

Determine the length of time, in years or months, as appropriate, for which you intend to receive your immediate annuity payments. Let "n" represent this number, for the number of time periods, either years or months, you'll be receiving payments. For example, if you want income from your immediate annuity for 10 years, you can elect to take 10 yearly payments or 120 monthly payments.


Step 4

Use this formula to compute your annual annuity immediate payment (p):

p = [P x i]/[1-(1+i)^-n]. For example, if you invest $50,000 at an 8 percent annual rate of interest, intending to receive payments for 10 years, you'll receive a yearly payment of [50,000 x .08]/[1-(1+.08)^-10] = $7451.47.


Step 5

Use this formula to compute your monthly annuity immediate payment (p):

p = [P x (i/12)]/[1-(1+i/12)^-n]. For example, if you invest $50,000 at an 8% annual rate of interest, intending to receive payments for 120 months, you'll receive a monthly payment of [50,000 x (.08/12)]/[1-(1+.08/12)^-120] = $606.64.


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Taking monthly annuity payments will yield a slightly lower annual total than yearly payments--for example, $7279.68 total for 12 monthly payments vs. $7541.47 for a yearly payment. This happens because the immediate annuity’s average balance is somewhat lower during the year than it is for the entire year. Most investors elect to receive monthly payments anyway, for a variety of reasons, including convenience and steady cash flow.