ordinary annuity

(noun)

An investment with fixed-payments that occur at regular intervals, paid at the end of each period.

Related Terms

Examples of ordinary annuity in the following topics:

  • Calculating Perpetuities

    • Perpetuities are a special type of annuity; a perpetuity is an annuity that has no end, or a stream of cash payments that continues forever.
    • Essentially, they are ordinary annuities, but have no end date.
    • Since there is no end date, the annuity formulas we have explored don't apply here.
    • To find the FV of a perpetuity would require setting a number of periods which would mean that the perpetuity up to that point can be treated as an ordinary annuity.
    • More accurately, is what results when you take the limit of the ordinary annuity PV formula as n → ∞.

  • Future Value of Annuity

    • The future value of an annuity is the sum of the future values of all of the payments in the annuity.
    • The future value of an annuity is the sum of the future values of all of the payments in the annuity.
    • For an ordinary annuity, however, the payments occur at the end of the period.
    • There are different FV calculations for annuities due and ordinary annuities because of when the first and last payments occur.
    • There are some formulas to make calculating the FV of an annuity easier.

  • Annuities

    • There are three advantages to making the loan an annuity.
    • Since annuities, by definition, extend over multiple periods, there are different types of annuities based on when in the period the payments are made.
    • Annuity-due: Payments are made at the beginning of the period .
    • Ordinary Annuity: Payments are made at the end of the period .
    • Mortgage payments are usually ordinary annuities.

  • Present Value of Annuity

    • Annuities-due have payments at the beginning of each period, and ordinary annuities have them at the end.
    • Recall that the first payment of an annuity-due occurs at the start of the annuity, and the final payment occurs one period before the end.
    • An ordinary annuity has annuity payments at the end of each period, so the formula is slightly different than for an annuity-due.
    • An ordinary annuity has one full period before the first payment (so it must be discounted) and the last payment occurs at the termination of the annuity (so it must be discounted for one period more than the last period in an annuity-due).
    • Both annuities-due and ordinary annuities have a finite number of payments, so it is possible, though cumbersome, to find the PV for each period.

  • Annuities and Mortgages

    • An annuity has two parts.
    • We define annuities as an ordinary annuity or an annuity due.
    • If a person pays into an annuity at the end of period, then it is an ordinary annuity.
    • For this chapter, we stick to ordinary annuities.
    • We also have the other side of an ordinary annuity.

  • Chapter Questions

    • You are saving for retirement, and plan to invest $2,000 every year into an ordinary annuity that earns 7% APR.Compute the value of your annuity in 20 years.
    • You have save an ordinary annuity with a balance of $50,000.Calculate your annual withdrawal payments if the annuity earns a 5% APR which you withdraw over 15 years.

  • Answers to Chapter 6 Questions

    • Using the formula for an ordinary annuity, we calculate the annuity value of $81,990.98 below:
    • Using the formula for an ordinary annuity, we calculate your annual payments as $4,817.11 below:

  • Calculating Annuities

    • Present Value (PV) - This is the value of the annuity at time 0 (when the annuity is first created)
    • Future Value (FV) - This is the value of the annuity at time n (i.e. at the conclusion of the life of the annuity).
    • The present value of an annuity can be calculated as follows:
    • For a growth annuity (where the payment amount changes at a predetermined rate over the life of the annuity), the present value can be calculated as follows:
    • The future value of an annuity can be determined using this equation:

  • Calculating the Yield of an Annuity

    • The yield of an annuity is commonly found using either the percent change in the value from PV to FV, or the internal rate of return.
    • The yield of annuity can be calculated in similar ways to the yield for a single payment, but two methods are most common.
    • The IRR is the interest rate (or discount rate) that causes the Net Present Value (NPV) of the annuity to equal 0.
    • Let's take an example investment: It is not technically an annuity because the payments vary, but still is a good example for how to find IRR:
    • Calculate the yield of an annuity using the internal rate of return method

  • Impact of Payment Frequency on Bond Prices

    • In other words, bond price is the sum of the present value of face value paid back at maturity and the present value of an annuity of coupon payments.
    • However, the present values of annuities of coupon payments vary among payment frequencies.
    • The present value of an annuity is the value of a stream of payments, discounted by the interest rate to account for the payments are being made at various moments in the future.
    • According to the formula, the greater n, the greater the present value of the annuity (coupon payments).