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Unformatted text preview: LECTURE 8 Annuities Osvaldo Lagares, M.S. 1 Annuities ³1R PDQ DFTXLUHV D SURSHUW\ without acquiring with it a OLWWOH DULWKPHWLF DOVR´ Ralph Waldo Emerson 2 3 Chapter Outline I. What Is an Annuity? II. Future Values of Annuities III. Sinking Funds IV. Present Values of Annuities V. Amortization Tables 4 5 What Is an Annuity? ¡ All of the situations we have considered so far, whether simple interest, simple discount, or compound interest, have had something in common. ¡ In every case, a sum of money is lent and then the loan is repaid in full all at once at the maturity date. ¡ However, take a car loan, for example. Suppose you borrow $14,500 at 8% compounded monthly for 5 years to buy a car. ¡ ,W¶V highly unlikely that you will get $14,500 up front, do nothing for 5 years, and then repay the entire loan. Instead, you would be making monthly payments. 6 What Is an Annuity? ¡ Definition An annuity is any collection of equal payments made at regular time intervals. ¡ Examples Ł Car loan Ł Student loan Ł Mortgage Ł Paycheck (salary) Ł Rent Ł Pension or Social Security ¡ These are NOT annuities: Ł Monthly credit card payment Ł Utility bills 7 What Is an Annuity? ¡ Definition A sum of money to which an DQQXLW\¶V payments and interest accumulate in the end is called the DQQXLW\¶V future value . A sum of money paid at the beginning of an annuity, to which the DQQXLW\¶V payments are accepted as equivalent, is called the DQQXLW\¶V present value . 8 What Is an Annuity? Example 1 ¡ Problem Ł Dylan deposits $25 from each paycheck into a 401(k) savings plan at work. He will keep this up for the next 40 years, at which time he plans to retire, hopefully having accumulated a large balance in his account. Since equal payments are being made into the account at regular intervals, this is an annuity. Is the value of the account when Dylan retires a present value or a future value? ¡ Solution Ł The value of the account when Dylan reaches retirement would be the future value. 9 What Is an Annuity? Example 2 ¡ Problem Ł Thalissa borrowed $160,000 to buy a house. To pay off this mortgage loan, she agreed to make payments of $1,735.52 per month for 30 years. Since her mortgage payments are all equal and are made at regular intervals, they constitute an annuity. Was the amount she borrowed this DQQXLW\¶V present value or future value? ¡ Solution Ł The $160,000 was received at the start of the annuity payments. Therefore, it would be the present value of the annuity. 10 What Is an Annuity? ¡ Definition An ordinary annuity is an annuity whose payments are made at the end of each time period. However, end of the month refers to a month counted from the date the annuity begins, not necessarily the end of the calendar month....
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 Spring '11
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