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

### Credit Cards, Interest, Loans, Retirement and Savings Plan

1. You have to charge $500 of car repairs and have no additional charges during the next two months. You will just pay the minimum payment each month for the next two months. The Annual Percentage Rate (APR) is 15.99% and the minimum payment each month is 4% of the balance. Determine the finance charge, new balance, and minimum

### Personal Financial Accounting

1. A company has $123,000 in Assets and $65,000 in Liabilities. How much does the company have in Stockholders' Equity? 2. Beginning Retained Earnings are $65,000, sales are $29,500, expenses are $33,000, and dividends paid are $3,500. How much is the amount in ending Retained Earnings? 3. The Notes Payable accoun

### 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

### Bond price, discount, amortization schedule & journal entries

For working capital your company has issued $1,500,000 in new bonds. The bonds have a stated 10% coupon rate with 5 annual interest payments of $150,000 due at the end of each year. At the time of issuance they were discounted to yield 12% to the investors, and your company will receive this discounted amount in cash. (a) Cal

### Computing Monthly Lease Payment

You are thinking about leasing a car. The purchase price of the car is $33000. The residual value (the amount you could pay to keep the car at the end of the lease) is $15000 at the end of 36 months. Assume the first lease payment is due one month after you get the car. The interest rate implicit in the lease is 6.75 APR, compou

### 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

### Distribution Possibility

An employer has a choice of how benefits will be distributed if it terminates its qualified plan. The plan can be designed to accommodate all of the following distribution possibilities except: A. The plan can purchase paid-up annuities from an insurance company. B. The plan can distribute benefits in cash or in kind if sto

### 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

### How much does Dr John need to invest at the end of each quarter?

Dr. John Doe is planning for his golden years. He will retire in 20 years, at which time he plans to begin withdrawing $50,000 annually to pay for his living expenses during retirement. He is expected to live for 30 years following her retirement. His financial advisor thinks he can earn 7% annually before his retirement and

### 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

### Annuity Payments and Pension Plans

Hunter retired last year and will receive annuity payments for life from his employer's qualified pension plan of $30,000 per year starting this year. During his years of employment, Hunter contributed $130,000 to the plan, and the total expected return based on his life expectancy is $200,000. All of the contributions were on a

### 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

### Calculating the quarterly installment of a car loan

You need to borrow $65,000 for a new car. The annual interest rate is 12%, compounded quarterly. You will be making quarterly payments for three years. 1. What is your quarterly payment? 2. How much will you owe on the loan after you make the first payment? 3. How much will you owe on the loan after you make the 2nd paym

### Present Value to Be Paid

Using a present value table, your calculator, or a computer program present value function, answer the following questions: a) What is the present value of nine annual cash payments of $4,000, to be paid at the end of each year using an interest rate of 6%? b) What is the present value of $15,000 to be paid at the end of 20

### Compound rate: Deposits at beginning or end of the year

If the business manager deposits $200 in a savings account at the end of each year for twenty years what will be the value of her investment: a) At a compounded rate of 10%? b) At a compounded rate of 20%? c) What would the outcome be if the deposits were made at the beginning of each year?