Minds On: Future ValueTom and Beth are twins. They save for retirement as follows:– Starting at age 25, Tom deposits $1000 at the end

of each year for 40 years– Starting at age 45, Beth deposits $2000 at the end

of each year for 20 yearsSuppose each annuity earns 8% per year compounded annually. Who will have the greater amount at retirement?

Present Value of an Annuity

LG: I can use a formula to calculate the present value of an annuity, given the regular payment

Present Value of an Annuity

• The present value of an annuity is the principal that must be invested today to provide the regular payments of an annuity

Formula for Present Value of an Annuity

– PV is the present value in dollars– R is the regular payment in dollars– i is the interest rate per compounding period, as a

decimal– n is the number of compounding periods

Example 1 – Retirement Savings• Howard plans to retire at age 60. He would like to have

enough money saved so that he can withdraw $3500 every month for 25 years, starting 1 month after he retires.

• If the account earns 9% per year, compounded monthly, how much money needs to be in the account when he retires to provide for the annuity?

Example 2 – Borrowing for a Loan• Shay plans to buy a used car. She can afford monthly

payments of $ 300. She is offered a lone at 6.9% interest per year, compounded monthly, for 3 years. He first payment is made 1 month after the car is purchased.a) What is most expensive car she can afford?b) How much interest will Shay pay on the loan?

Borrowing for a LoanMost loans are repaid by making equal monthly payments over a fixed period of time. These payments form an annuity whose present value is the principal borrowed. When all of the payments are made, both the principal and interest have been repaid

Homework

• Pg. 423 # 2, 6, 8-10• Quiz Friday: Future and Present Value of an

annuity