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Annuities MATH 102 Contemporary Math S. Rook

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Overview Section 9.4 in the textbook: – Annuities – Sinking funds

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Annuities

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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

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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

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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

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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?

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Sinking Funds

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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

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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?

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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?

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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)

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