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Published byMalcolm Lyons Modified over 3 years ago

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Regular Deposits And Finding Time

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An n u i t y A series of payments or investments made at regular intervals. A simple annuity is an annuity in which the payments coincide with the compounding period. An ordinary annuity is an annuity in which the payments are made at the end of each interval.

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From previous lessons, you have learned how to find... Future Value of Compounding Interest Future value, A, of the amount invested (in dollars $) at the beginning, $P, at the end of n compounding periods. P = Amount Invested r = Interest Rate Per Period n = Number Of Compounding Periods P = Amount Invested r = Interest Rate Per Period n = Number Of Compounding Periods

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Future Value of an Annuity (Formula #1) Future value of ALL investments until the LAST compounding period. a = Amount Invested Each Period r = Interest Rate Per Period n = Number Of Compounding Periods a = Amount Invested Each Period r = Interest Rate Per Period n = Number Of Compounding Periods The formula for the Sum of a Geometric Series can be used to determine the future value of an annuity.

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Future Value of an Annuity (Formula #2) Future value of annuity in which $R is invested at the end of each n compounding periods earning i% of compound per interval is:

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Now that we know how to find FV, we can now find the values of : R The regular payment of an annuity required to reach future value n The number of compounding periods to reach future value t The term (number of years to pay off) of an annuity.

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Example 1 Sam wants to make monthly deposits into an account that guarantees 9.6 %/a compounded monthly. He would like to have $500 000 in the account at the end of 30 years. How much should he deposit each month? First, we must calculate i and n according to the compounding period : i = 9.6% = 0.096 / 12 = 0.008 n = 30 yrs = 30 x 12 = 360 FV = $500 000 We are now solving for r : r = $ ?

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Now we are able to solve for R, or the amount Sam should be depositing each month: Sam would have to deposit $240. 80 into the account each month in order to have $500 000 at the end of 30 years.

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Example 2 Nahid borrows $95 000 to buy a cottage. She agrees to repay the loan by making equal monthly payments of $750 until the balance is paid off. If Nahid is being charged 5.4%/a compounded monthly, how long will it take her to pay off the loan? First, we must calculate i according to the compounding period : i = 5.4% = 0.054 / 12 = 0.0045 PV = $95 000 R = $750 We are now solving for n : n = ? yrs

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Take a look at your handout for solution.

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