This website uses cookies to ensure you have the best experience.

# Annuity & Perpetuity Essay

1112 words - 5 pages

Annuity
Annuity is a special case of multiple cash flows where:
* The cash flows are equal for a fixed period of time.
* The cash flows are at the end of each period.
The equal amount of cash flows is called annuity payment or payment (C).

You can solve an annuity problem the same way as multiple cash flows, calculating the value of each cash flow and sum all values. However, this can be quite tedious especially when dealing with long series of annuity payments. Fortunately, future and present values of annuity payments can be calculated from the following equations:
or
Where:
* FVA = future value of annuity
* PVA = present value of annuity
* C = amount ...view middle of the document...

Thus the PVA and FVA equations cannot be applied.

Note: There are three payments (c) and five time periods (t).
Perpetuity
Perpetuity is similar to annuity. The only difference between annuity and perpetuity is the ending period. For annuity, payments last for a certain period, whereas for perpetuity, they continue indefinitely, as represented by (∞).

The equation below is used to calculate present value of perpetuity. It requires only the first payment and interest rate.

where…
* PV(∞) = present value of perpetuity.
* C = the first payment
* r = interest rate per period

For example, an insurance company has just launched a security that will pay \$150 indefinitely, starting the first payment next year. How much should this security be worth today if the appropriate return is 10%? Using the time line below, complete the PV(∞) equation.

The equation below is used to calculate present value of perpetuity. It requires only the first payment and interest rate.

* PV(∞) = ?
* C = 150
* r = .10

*A perpetuity is a type of annuity.
Normally, an annuity pays something back each year and then returns your principal at the end of a number of years. A perpetuity gives you a payment each year forever and never gives you your money back. The converge in present value at the length of the annuity increases because, let's face it, getting your principal back in 99 years is pretty close to not getting it back at all. If you don't believe me, play with the present value function in excel.

Differences Between an Annuity & a Perpetuity

Britt Barclay
Christian Barclay is currently an undergraduate in the Farmer School of Business at Miami University of Ohio. He has research experience in the field of chemical engineering and interned this previous summer at the Four Seasons Nile Plaza in Cairo, Egypt. He has written for Demand Studios since May 2009 and has been published on eHow.com and Golflink.com.
By Britt Barclay, eHow Contributor | updated October 25, 2011

Annuities and perpetuities are both types of payment schedules; these schedules are most often plans to settle a debt. Payments on these debts are made at regular intervals. One of these intervals is considered one period. Annuities and perpetuities are used by...

## Other Papers Like Annuity & Perpetuity

### Accounting Vocabularies Essay

974 words - 4 pages flows occur at the beginning of the period. Perpetuity: An annuity in which the cash flows continue forever. Perpetuity is also called consol (in Canada & UK). Preferred stock is an important example of it. Effective Interest Rate (EIR): The actual paid on a loan, or earned on a deposit account, depending on the frequency of compounding or effect of inflation. It is different from the nominal rate of interest which ignores compounding and

### All American Pipeline Essay

2454 words - 10 pages Project. Once we obtained the UFCF, the terminal value was calculated in three different ways, treating the pipeline as an asset on our books, finding the value of project if cash flows are received for perpetuity an finding the annuity value of cash flows for 30 years by assuming that after 1992 cash flows go on for 30 years. We did this to show a sensitivity analysis, but from our results we observed that values calculated from all the three

### How Do You Define A Competitive Strategy (Strategies) In Best Buy

9833 words - 40 pages family can lead a good life. How much would you need to save in your retirement fund to achieve this goal (assume that the perpetuity payments starts on the day of retirement. The interest rate is 10%)? A) \$1,000,000 B) \$1,100,000 C) \$2,000,000 D) None of the above Answer: B Type: Difficult Page: 37 Response: PV = (100,000/0.1)(1.1) = 1,100,000 19. An annuity is

### Foundations of Finance 1

714 words - 3 pages +R)T = \$550(1+0.055)10 = \$939.48, which is less than \$1,000. 4. If annual interest rate is 5%: (a) PV = C*(PV factor) = C*[1-(1/(1+R)T)]/R = (\$10,000/0.05)*[1-(1/(1+0.05)6)] = \$50,756.92 (b) PV = C/R = \$10,000/0.05 = \$200,000 -To compare with the present value of the annuity, the perpetuity needs to be discounted PV/(1+R)T = \$200,000/(1+0.05)10 = \$122,782.65 At interest rate of 5%, I prefer the perpetuity (b). If annual interest rate is 10

### Operation Management

792 words - 4 pages ? QUESTION 6 You have a chance to buy an annuity that pays RM1,000 at the end of each year for 5 years. You could earn 6% on your money in other investments with equal risk. What is the most you should pay for the annuity? QUESTION 7 What’s the present value of a perpetuity that pays RM100 per year if the appropriate interest rate is 6%? QUESTION 8 What’s the rate of return you would earn if you paid RM1,500 for a perpetuity that pays RM105

### Time Value Money

2905 words - 12 pages the PV of a 5-year annuity due of \$600 payments at 7%? Yet again, set your calculator into BGN mode and put in the data: 5 N, 600 PMT, 7 I/Y, CPT PV. This is presently worth \$2,632.33. The PV of ordinary annuity is \$2,460.12 so this proves that both FVA due and PVA due are worth more than FVA and PVA. Perpetuity is a special annuity that has a specified beginning date but never ends. Since there is no end, the equation is One problem is that this

### Exam Formula Sheet Spring 2010

575 words - 3 pages SOME USEFUL FORMULAS Rights R + S = X R = {N( M-S )}/(N+1 ) X = ( NM + S )/(N+1 ) Financial Future Value FV = PV (1 + i)n Present Value PV = FV (1 + i)-n Annuity Future Value FV = PMT {[(1 + i)n - 1]/ i} Annuity Present Value PV = PMT {[1 - (1 + i)-n]/ i} Perpetuity PV = Pmt /i Dividends No growth P0 = d1 /r Dividends constant growth P0 = d1 /(r - g) Effective interest rate ie = (1 + i)m - 1 Net

### Myob Report

3726 words - 15 pages , n – the number of payments to be made on the loan, PMT – the periodic payment (annuity) to be made on the loan. Using the PV of an annuity formula: you would find the amount of the loan outstanding at a point in time, i.e. the loans PV. From this you would multiply the amount outstanding by the interest rate per period (r) to find the interest component of the PMT. You would then subtract the interest component from the PMT and this would

### Capital Markets

1656 words - 7 pages ( 7.44 5. You are willing to pay \$15,625 now to purchase a perpetuity which will pay you and your heirs \$1,250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be willing to pay if this were a 20-year, annual payment, ordinary annuity instead of a perpetuity? Solution: To find your yield to maturity, Perpetuity value ( PMT/I. So, 15625 ( 1250/I. I ( 0.08

### Bond Valuation

1462 words - 6 pages last year was included as a part of the present value of an annuity calculation while the par value was discounted as a lump sum of \$1,000. As indicated, the value of the bond when only four years to maturity remain is only \$1,066.21. This is a decrease in value of \$13.66. When expressed as a percentage of the original value of \$1079.87, this represents a loss of 1.26%. The total return of 8% that we built into our valuation when the bond had

### Final Exam Key

2462 words - 10 pages 10 equal installments. In the other case, we’re told that the \$ 80 million will be paid in 10 installments, but the installments will increase by 5 percent per year. Who got the better deal? Because if the time-value-of-money the better deal is the one with equal installments. 12. A 5- year annuity of ten \$ 7,000 semiannual payments will begin 8 years from now, with the first payment coming 8.5 years from now. If the discount rate is 10

## Related Essays

### Statistic Essay

518 words - 3 pages final lump sum. d. Ordinary annuity- an annuity whose payments occur at the end of each period. Annuity due- If payments are paid in the beginning of each period, then we have an annuity due. e. Perpetuity- is an annuity with an infinite number of payments. Consul- it promises to pay interest perpetually, they are called perpetuities. Perpetuity is a simply an annuity with an extended life. f. Outflow- the

### Fnce 100 Essay

2556 words - 11 pages 11 Growing Perpetuities  A growing perpetuity is a stream of cash flows that grow at a constant periodic rate, g, with no end. Cash Flows 0 Periods 0  C C(1+g) 1 C(1+g)4 2 3 C(1+g)5 … 5 C(1+g)2 C(1+g)3 6 … 4 Infeasible to calculate by brute force - is there a shortcut? PV  C rg » You should be able to derive this 23 Annuities  An annuity is a level stream of regular

### Fin100 Quiz4 Essay

1962 words - 8 pages | | | | | Selected Answer: |   compound interest. | Correct Answer: |   compound interest. | | | | | * Question 4 2 out of 2 points | | | The present value of a \$20,000 perpetuity at a 7 percent discount rate isAnswer | | | | | Selected Answer: |   \$285,714. | Correct Answer: |   \$285,714. | | | | | * Question 5 0 out of 2 points | | | Which of the following terms best describes an annuity due?Answer

### Finance Questions Essay

648 words - 3 pages Compound Interest the situation in which interest paid on an investment during the first period is added to the principal. During the second period, interest is earned on the original principal plus the interest earned during the first period. number of years Annuity a series of equal dollar payments made for a specified Annuity Due annuity in which the payments occur at the beginning of each period Perpetuity an annuity with an infinite