In finance, an annnuity is a stream of periodic, fixed payments received over a specific period of time. We use time value of money concepts, such as present value and future value, to value this stream of payments. A perpetuity is an annuity that continues forever - or at least indefinitely into the future. We use a modification of the formula for present value of a perpetuity to value and annuity.

The present value of a perpetuity is simply equal to the payment, C, divided by the rate of interest.

The present value of an annuity is equal to the present value of the equivalent perpetuity; however, we subtract a second perpetuity equal to the amount that the additional stream of payments would have been worth if they had not stop at the specified date. We can simplify this formula as follows:

The portion of the formula that appears after the C is often referred to as the *annuity factor. *Annuity factors are often presented in table form to allow for easy calculations for the present value of the annuity.

The future value of an annuity can be found similarly:

An ordinary annuity refers to an annuity that has its first payment one year from now. It is contrasted with an annuity due, which has an immediate first payment. In order to find the present or future value of an annuity due, we multiply the value of the ordinary annuity by (1+r), in order to 'bring the cash flows forward one period.'

# Annuity

### NVP versus IRR

here are the cash flows for two mutually exclusive projects Project C0 C1 C2 C3 A (20,000) 8,000 8,000 8,000 B (20,000) 0 0 25,000 a) at what interest rates would you prefer project A to B b) what is the IRR of each of each project the response has to be in excel format

### Savings Plan decisions for your Pension

1) You work for a company that provides a pension plan to which the company contributes 50 percent of the amount you contribute. For example, if you specify that $1000 of your annual salary is to go into the plan, the company will add $500 to make the total contribution $1500 per year. The plan guarantees an annual rate of retur

### Various Investment-Based Problems

1. A saver places $1,000 in a certificate of deposit that matures after 20 years and that each year pays 4 percent interest, which is compounded annually until the certificate matures. a) How much interest will the saver earn if the interest is left to accumulate? b) How much interest will the saver earn if the interest is wit

### Questions for Surveys

See the attached file. Please help in completing a research proposal for a financial services industry (USAA). The outline must include details for each of the following 7 sections. Questions for Surveys/Questionnaires/Interviews . Implications and Limitations Participants Hypothes

### Yields, Coupon Rates, Bonds, etc

Even though most corporate bonds in the United States make coupon payments semiannually, bonds issued elsewhere often have annual coupon payments. Suppose a German company issues a bond with a par value of €1,000, 15 years to maturity, and a coupon rate of 6.5 percent paid annually. If the yield to maturity is 7.6 percent,

### Finance and accounting questions

1. Notes payable—discount basis On August 1, 2013, Colombo Co.'s treasurer signed a note promising to pay $120,000 on December 31, 2013. The proceeds of the note were $114,000. Required: a. Calculate the discount rate used by the lender. b. Calculate the effective interest rate (APR) on the loan. c. Use the horiz

### Risk Profiles for Investors

Given an individual risk profile, be it an aversion to risk or a high tolerance for risk; and, the current relatively low level of interest rates would he invest today in an asset, like a US Government Bond, that has a long term fixed cash flow associated with it? Remember to consider the investment time frame and investment pu

### Business Mathematics: Compound Interest and Investment Advice

Individual Work 1 Consider the concept of compound interest you read about this week. Now, apply your knowledge of these models to a practical problem. Please respond to all of the following prompts in the class discussion section of your online course: 1. You have been asked by your friend to describe this topic. Your frie

### Rent and Interest Calculations for a Corporation

1. You can choose between the following rent payments: (a) A lump sum cash payment of $100,000 (b) 10 annual payments of $12,000 each, the first occurring immediately. (c) 120 monthly payments of $1,200 each. the first occurring immediately. (Friendly suggestion: this is a lot easier to calculate on a computer spreadshee

### Estimate the Percentage of Salary Contributed to Pension Plan

Suppose that in a certain defined benefit pension plan: A. Employees work 45 years earning wages that increase at a real rate of 2% B. They retire with a pension equal to 70% of their final salary. This pension increases at the rate of inflation minus 1% C. The pension is receives for 18 years. D. The pension fund's income

### Determining a Lease

Kingdom Leasing Inc. agrees to lease jousting equipment to Knight Inc. on Jan 1, 2012. They agree on the following terms: 1) The normal selling price of the jousting equipment is $325000 and the cost of the asset to Kingdom Leasing Inc. was $250000. 2) Knight will pay all maintenance, insurance and taxes costs directly and

### Annuity Concepts

Beginning three months from now, you want to be able to withdraw $1,700 each quarter from your bank account to cover college expenses over the next 4 years. The account pays 1.25 percent interest per quarter. How much do you need to have in your account today to meet your expense needs over the next 4 years? $24,514.50 $2

### Calculating the Rate of Return for Annuities

Your insurance agent is trying to sell you an annuity that costs $230,000 today. By buying this annuity, your agent promises that you will receive payments of $1,225 a month for the next 30 years. What is the rate of return on this investment?

### Insurance Settlement Payments

1.) You are considering three insurance settlement offers. The first offer includes annual payments of $5,000, $10,000, $15,000, etc., where the payment for each year is $5,000 more than the payment for the previous year, over the next ten years. The first payment of $5,000 will be made exactly one year from today and the last p

### Impacts on Nominal Interest Rates

- Explain how inflation or purchasing power impacts stated or nominal interest rates. - create a personal scenario that exemplifies the time value of money that includes the opportunity cost involved. - Discuss the pros and cons of annuities when compared with other financial instruments and whether they provide a better i

### Valuation Models

1. Jean Splicing will receive $50,000 in 50 years or $2,000 today. If long-term rates are 7 percent, what choice would you recommend? a. What is the current value of the future payments b. What is the current value, if they are received at the beginning of each year? 2. "Red" Herring will receive $11,000 a year for the next

### ERISA Regulated Plans

Does ERISA regulate mandated benefits such as Social Security benefits as well as voluntary benefits provided by employers? Donovan v. Dillingham, 1982 U.S. Court of Appeals decision (precedent) A "plan" under ERISA exists if a reasonable person can determine: The intended benefits A class of beneficiaries The sources of

### Tax Planning - Roth Case

The Roth Case Tax Planning Your clients, Ira and Flora Roth, have come to you for some basis tax planning advice and guidance. Here are the facts you need to help them. • Ira's earned income: $65,000 • Flora's earned income: $52,000 • They live in Kansas and own a municipal bond issued by the city of Wichita

### Annuity Payments from Insurance Policy

Sarah is age 73 and has a great deal of difficulty living independently, as she suffers from severe arthritis. She is covered by a $400,000 life insurance policy payable upon death, and her children are named as the beneficiaries. Because of her health, Sarah decides to live in a nursing home, but she does not have enough income

### Initial Investment - Determine the Present Value of Future Annuities

a) Think of something you want or need for which you currently do not have the funds for. It could be a vehicle, boat, horse, jewelry, property, vacation, college fund, retirement money, etc. Select something which costs somewhere between $2,000 and $50,000. Use the "Present Value Formula", which computes how much money you nee

### Bonds - Holding Period Yield

Your boss has again asked for your help. He needs to figure out the holding period yield on a candidate bond for inclusion in a pension bond portfolio and whether your company should purchase it. He has left a note on your desk: We are considering purchasing a 7% percent coupon bond (coupons paid semiannually) with 14 years rem

### Loan, Corporate, Time Value of Money Questions

1. A $50,000 loan is to be amortized over 7 years, with annual end-of-year payments. Which of these statements is CORRECT? The annual payments would be larger if the interest rate were lower. If the loan were amortized over 10 years rather than 7 years, and if the interest rate were the same in either case, th

### Separation of ownership and management, shareholder goals, bonds, interest

Problem 1-6: In most large corporations, ownership and management are separated. What are the main implications of this separation? Problem 1-8: We can imagine the financial manager doing several things on behalf of the firm's stockholders. For example, the manager might:

### Finance Calculations using Excel: Future Value and Present Value

1. You want to buy a car, and a local bank will lend you $ 20,000. The loan would be fully amortized over 5 years ( 60 months), and the nominal interest rate would be 12%, with interest paid monthly. What is the monthly loan payment? What is the loan's EFF%? 2. Your parents will retire in 15 years. They currently have $ 230,000

### Calculating the periodic amounts

1. Lily Henry wants to buy her son a car for his 21st birthday. If Lily's son is turning 16 today, and interest is 8% per annum, compounded semiannually, what would Lily's semiannual investment need to be if the car will cost $30,000 and the first payment is made six months from today? 2. Determine the amount of the specific

### Assorted problems in Finance

1. Jane Alexander currently has $,7,750 in a money market account paying 7.25% annually. She plans to use this amount and her savings over the next 5 years to make a down payment on a house. She estimates that she will need $20,000 in 5 years. How much should she invest in the money market account semi-annually over the next 5 y

### Present Value Problem Set: Annuities

Find: - the present value of $300,000 annuity at 6% for 20 years - the present value of $500,000 deferred annuity at 6% for 20 (21-40) years - the present value of 50,000 annuity at 6% for 40 years - the present value of 75 million paid at the end of 40 years - the present value of 300,000 annuity at 11% for 20 years - th

### Arroyo Fresco Case Study

Analyze the organization and develop a new organizational strategy for the Arroyo Fresco Community Health Center. The strategy should be formulated using the information from the case study, including an analysis of the results, and should take into account current concerns including health care reform, the political environment

### Future value of single sum

1.) You put $5,000 in an investment account today which will earn 6% over the next 11 years, what is the future value? 2.) You put $2,000 in an investment account today which will earn 8% over the next 14 years, what is the future value? 3.) You deposit $5,000 into a retirement account at the end of the next 15 years earni

### Present and future value of single sum, perpetuity, and present value of annuity

1. Present value of single sum problem You are going to be given $100,000 in 12 years. Assuming an inflation rate of 3.5%, what is the present value of this amount? 2. Perpetuity problem What is the value of a perpetuity with an annual payment of $100 and a discount rate of 6%? 3. Future value of single sum problem