annuity

Examples of annuity in the following topics:

• 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 annuity-due, the payments occur at the beginning of each period, so the first payment is at the inception of the annuity, and the last one occurs one period before the termination.
  • 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.

• 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:

• 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.
  • The PV of an annuity-due can be calculated as follows:
  • An ordinary annuity has annuity payments at the end of each period, so the formula is slightly different than for an annuity-due.
  • Credit is receiving a sequence of payments, or an annuity, of $1,000 per month, its future value is given by the annuity formula:

• 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.
  • More accurately, is what results when you take the limit of the ordinary annuity PV formula as n → ∞.
  • It is also possible that an annuity has payments that grow at a certain rate per 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.
  • However, if a person pays into an annuity at the beginning of the period, he or she receives one extra payment that earns interest over the life of the annuity, called an annuity due.
  • Calculate the value of your annuity in five years if you pay $20,000 into the annuity.

• 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).

• Present Value, Multiple Flows

  • The calculations get markedly simpler if the cash flows make up an annuity.
  • In order to be an annuity (and use the formulas explained in the annuity module), the cash flows need to have three traits:
  • The annuity formulas are good for determining the PV at the date of the inception of the annuity.
  • If you do, that supposes that both annuities begin on 1/1/13, but neither do.
  • Instead, you have to first find the PV of the first annuity on 1/1/14 and the second on 1/1/15 because that's when the annuities begin.

• Future Value, Multiple Flows

  • Investments that have these three traits are called "annuities. "
  • There are formulas to find the FV of an annuity depending on some characteristics, such as whether the payments occur at the beginning or end of each period.
  • There is a module that goes through exactly how to calculate the FV of annuities.
  • If the multiple cash flows are a part of an annuity, you're in luck; there is a simple way to find the FV.