MATH 102 Contemporary Math S. Rook Annuities MATH 102 Contemporary Math S. Rook

Overview Section 9.4 in the textbook: Annuities Sinking funds

Annuities

Annuities Annuity: an interest-bearing account where we make a series of regular deposits of the same amount Ordinary Annuity: depositing the same amount at the end of every compounding period Observe that the problem of calculating the value of an annuity is different from Section 9.2: In Section 9.2, we deposited ONE lump sum into an account and compounded interest In this section, we are depositing the same amount into the account at regular intervals Earlier deposits will gain more interest than later ones

Annuities (Continued) We will be dealing only with ordinary annuities The amount A that is present in the annuity at time t (in years) where R is the amount of deposit, n is the number of compounding periods per year, and r is the annual interest rate of the account is For theory refer to pages 423-4 of the textbook Essential idea is that earlier deposits accumulate more interest than later deposits Do not be intimidated by the formula – perform the calculations in steps instead of all at once See page 425 in the textbook

Annuities (Example) Ex 1: Calculate the value of the annuity: a) Amount to deposit, $200; compounded monthly; annual rate of 3%; over 8 years b) Amount to deposit, $500; compounded monthly; annual rate of 7.5%; over 12 years

Annuities (Example) Ex 2: Matt is saving to buy a new Vespa scooter. If he deposits $75 at the end of each month into an account that pays an annual interest rate of 6.5%, how much will he have saved in 2.5 years?

Sinking Funds

Sinking Funds Sink Fund: an account where deposits are made regularly to meet a financial goal Again, different from Section 9.2 Idea is to save up the entire purchase price so we will not go into debt Another type of annuity so no need to learn a new formula Instead of answering the question “how much will I have,” a sink fund answers the question “how much do I need to put in regularly?” Naturally, we can estimate the regular amount to deposit, but this ignores the accruing interest

Sinking Funds (Example) Ex 3: Kanye wants to save $14,000 in 8 years by making monthly payments into an ordinary sink fund for a down payment on a condominium. If the fund pays 8.4% interest annually, what will his regular monthly payment be to meet his goal?

Sinking Funds (Example) Ex 4: Sandra Lee is making monthly payments into a sink fund. She wants to have $600 in the fund in 6 months in order to buy an oven for her delicious baked goods. If the account pays an annual interest rate of 8.2%, what regular monthly payment would allow her to meet her goal?

Summary After studying these slides, you should know how to do the following: Calculate the amount in an annuity Calculate required payments in a sink fund to meet financial goals Additional Practice: See problems for Section 9.4 Next Lesson: Amortization (Section 9.5)