Most of the people use an annuity as a retirement tool (pension) that guarantees steady income in the coming years. An equal amount should be paid or received as an annuity and the time lag between payments occurring consecutively should be same.
There is a difference between ordinary annuity and annuity due which lies in the timing of the two annuities. So, the article makes an attempt to shed light on the differences between the two, have a look.
Content: Ordinary Annuity Vs Annuity Due
Comparison Chart
Basis for ComparisonOrdinary AnnuityAnnuity DueMeaningOrdinary annuity is one in which the inflow or outflow of cash fall due for payment at the end of each period.Annuity due is described as the series of cash flows occurring at the beginning of each period.PaymentBelongs to the period preceding its date.Belongs to the period following its date.Appropriate forPaymentsReceiptsExampleHousing loan, payment of mortgage, coupon bearing bonds, etc.Rental lease payments, life insurance premium, etc.Definition of Ordinary Annuity
Ordinary Annuity is defined as a series of regular payments or receipts; that occurs at regular intervals over a specified number of periods. It is also known as annuity regular or deferred annuity.
In general, ordinary annuity payment is made on a monthly, quarterly, semi-annual or annual basis. The present value of the ordinary annuity is computed as of one period prior to the first cash flow, and the future value is computed as of the last cash flow.
Formula:
- Present Value (PV) of ordinary annuity: PMT × ((1 – (1 + r) ^ -n ) / r)
where, PMT = Period cash payment
r = Interest rate per period
n = Total number of periods
Definition of Annuity Due
Annuity Due or immediate is nothing but the sequence of periodic cash flows (payments or receipts) regularly occurring at the end of each period overtime. The first cash flow of the annuity falls due at the present time. The most common example of an annuity due is the rent, as the payment should be made at the start of the new month.
As in the case of an ordinary annuity, the present and future values of the annuity due are also calculated as first and last cash flows respectively.
Formula:
- Present Value (PV) of Annuity Due: PMT + PMT × ((1 – (1 + r) ^ -(n-1) / r)
where, PMT = Period cash payment
r = Interest rate per period
n = Total number of periods
Key Differences Between Ordinary Annuity and Annuity Due
The points given below are noteworthy, so far as the difference between ordinary annuity and annuity due is concerned:
- Ordinary annuity refers to the sequence of steady cash flow, whose payment is to be made or received at the end of each period. Annuity due implies the stream of payments or receipts which fall due at the beginning of each period.
- Each cash inflow or outflow of an ordinary annuity is related to the period preceding its date. On the contrary, an annuity due, represent the cash flow period following its date. As the cash flows belonging to annuity due occur one period earlier than that of an ordinary annuity.
- An ordinary annuity is best when an individual is making payment whereas annuity due is appropriate when a person is collecting payment. As the payment made on annuity due, have a higher present value than the regular annuity. This is because of the principle of time value of money, i.e. the value of one rupee, today is greater than the value of one rupee, after one year.
- Payment of car loan, payment of mortgage and coupon bearing bonds are some examples of an ordinary annuity. On the flip side, the common examples of an annuity due are rental lease payments, car payments, payment of life insurance premium and so on.
Conclusion
Annuity aims at providing a constant stream of income to the annuity holder for a long time. An individual can make a choice between these two annuities considering some factors, such as the income that he wants during retirement and the degree of risk he is able to take.
Click the box below each question to see the correct answer. Keep track of how many you answer correctly and compare the total to the grading scale found at the bottom of the page.
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1. A 5-year ordinary annuity has a present value of $1,000. If the interest rate is 8 percent, the amount of each annuity payment is closest to which of the following?A. $250.44
B. $231.91
C. $181.62
D. $184.08
E. $170.442. An 8-year annuity due has a present value of $1,000. If the interest rate is 5 percent, the amount of each annuity payment is closest to which of the following?
A. $154.73
B. $147.36
C. $109.39
D. $104.72
E. $ 99.743. A 5-year ordinary annuity has a future value of $1,000. If the interest rate is 8 percent, the amount of each annuity payment is closest to which of the following?
A. $250.44
B. $231.91
C. $184.08
D. $181.62
E. $170.444. An 8-year annuity due has a future value of $1,000. If the interest rate is 5 percent, the amount of each annuity payment is closest to which of the following?
A. $104.72
B. $109.39
C. $147.36
D. $154.73
E. $ 99.745. Which of the following statements is TRUE? (Assume that the yearly cash flows are identical for both annuities and that the common interest rate is greater than zero.)
A. The present value of an annuity due is greater than the present value of an ordinary
annuity.
B. The present value of an ordinary annuity is greater than the present value of an annuity
due.
C. The future value of an ordinary annuity is greater than the future value of an annuity
due.
D. Both B and C are correct.6. A 5-year ordinary annuity has periodic cash flows of $100 each year. If the interest rate is 8 percent, the present value of this annuity is closest to which of the following?
A. $331.20
B. $399.30
C. $431.24
D. $486.65
E. $586.707. A 5-year annuity due has periodic cash flows of $100 each year. If the interest rate is 8 percent, the future value of this annuity is closest to which of the following equations?
A. ($100)(FVIFA at 8% for 5 periods)
B. ($100)(FVIFA at 8% for 4 periods)(1.08)
C. ($100)(FVIFA at 8% for 5 periods)(1.08)
D. ($100)(FVIFA at 8% for 5 periods) + $100
E. ($100)(FVIFA at 8% for 4 periods) + $1008. A 5-year annuity due has periodic cash flows of $100 each year. If the interest rate is 8 percent, the present value of this annuity is closest to which of the following equations?
A. ($100)(PVIFA at 8% for 4 periods) + $100
B. ($100)(PVIFA at 8% for 4 periods)(1.08)
C. ($100)(PVIFA at 8% for 5 periods)(1.08)
D. ($100)(PVIFA at 8% for 6 periods) - $100
E. Both A and C9. Study the time line and accompanying 5-period cash-flow pattern below.
0 1 2 3 4 5 6 Time line
|--------|--------|--------|--------|--------|--------|
$10 $10 $10 $10 $10 Cash flows
¦ ¦
A B
The present value of the 5-period annuity shown above as of Point A is the present value of a 5-period ______________ , whereas the future value of the same annuity as of Point B is the future value of a 5-period ______________ .
A. ordinary annuity; ordinary annuity.
B. ordinary annuity; annuity due.
C. annuity due; annuity due.
D. annuity due; ordinary annuity.
0 1 2 3 4 5 6 Time line
|--------|--------|--------|--------|--------|--------|
$10 $10 $10 $10 $10 ¦ Cash flows
¦ ¦
A B
The present value of the 5-period annuity shown above as of Point A is the present value of a 5-period ______________ , whereas the future value of the same annuity as of Point B is the future value of a 5-period ______________ .
A. ordinary annuity; ordinary annuity.
B. ordinary annuity; annuity due.
C. annuity due; annuity due.
D. annuity due; ordinary annuity.
How did you do?
- All 10 correct = You are an annuity GURU! Congratulations!
- 8 or 9 correct = Approaching zero defects -- just review what you missed.
- 6 or 7 correct = You need a little more work. Review page 2; then take the quiz again.
- 5 or fewer correct = You have some work to do: (a) review page 2; (b) try your hand at the practice time-value-of-money annuity problems (with answers and detailed solutions) found at: //web.utk.edu/~jwachowi/annuity_prob.pdf ; and (c) then take the quiz again.