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Warm up You took out a loan for $1460 and the bank gave you a 5 year add on loan at an interest rate of 10.4%. How much interest will you pay and how much will your monthly payments be? Using the unpaid balance method find the finance charge, and next months balance. Last months balance is $475 at an interest rate of 21%. You bought a jacket for $180, returned a camera for $145 and made a payment of $225.

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Annuities © 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 2 9.4 Calculate the future value of an ordinary annuity. Perform calculations regarding sinking funds.

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 3 Annuities An annuity is an interest-bearing account into which we make a series of payments of the same size. If one payment is made at the end of every compounding period, the annuity is called an ordinary annuity. The future value of an annuity is the amount in the account, including interest, after making all payments.

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What is an annuity? An annuity is a contract between you and an insurance company that is designed to meet retirement and other long-range goals, under which you make a lump-sum payment or series of payments. In return, the insurer agrees to make periodic payments to you beginning immediately or at some future date.

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Here’s a little more on annuities…. https://www.fidelity.com/annuities/FPRA- variable-annuity/video http://www.youtube.com/watch?v=w9e0BYLIq gs

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 6 Annuities

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Example: A payment of $50 is made at the end of each month into an account paying a 6% annual interest rate, compounded monthly. How much will be in that account after 3 years? Annuities

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 8 Example: A payment of $50 is made at the end of each month into an account paying a 6% annual interest rate, compounded monthly. How much will be in that account after 3 years? Solution: Annuities We see that R = 50, = and n = (continued on next slide)

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 9 Annuities Using the formula for finding the future value of an ordinary annuity, we get

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 10 Annuities Suppose that in January you begin making payments of $100 at the end of each month into an account paying 12% yearly interest compounded monthly. (continued on next slide)

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You will create a table like the one in the example showing an annuity with a monthly deposit of $250 at the end of each month, compounded monthly at 14.5%. For the rate, use accuracy to 3 decimal places.

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 12 You may want to save regularly to have a fixed amount available in the future. The account that you establish for your deposits is called a sinking fund. Because a sinking fund is a special type of annuity, it is not necessary to find a new formula. We can use the formula for calculating the future value of an ordinary annuity that we have stated earlier. In this case, we will know the value of A and we will want to find R. Sinking Funds

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 13 Example: Assume that you wish to save $1,800 in a sinking fund in 2 years. The account pays 6% compounded quarterly and you will also make payments quarterly. What should be your monthly payment? Recall the formula for finding the future value of an ordinary annuity: (continued on next slide) Sinking Funds

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 14 Sinking Funds We see that A = 1,800, = and n =

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 15 Example: Suppose you have decided to retire as soon as you have saved $1,000,000. Your plan is to put $200 each month into an ordinary annuity that pays an annual interest rate of 8%. In how many years will you be able to retire? (continued on next slide) Sinking Funds

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 16 Example: Suppose you have decided to retire as soon as you have saved $1,000,000. Your plan is to put $200 each month into an ordinary annuity that pays an annual interest rate of 8%. In how many years will you be able to retire? (continued on next slide) Sinking Funds Solution: We see that A = 1,000,000, = and R = 200.

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© 2010 Pearson Education, Inc. All rights reserved.Section 9.4, Slide 17 Sinking Funds We solve this equation for n.

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Homework, Page 341 Find the amount A accumulated after investing a principal P for t years at an interest rate of r compounded annually. 1.

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