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When investing, people usually do not simply deposit one lump sum and wait several years for it to earn interest. Instead, they make regular payments (often deducted from their pay checks). These types of investments are called . Definitions::Payments of equal value made at equal times periods. :A sum of money paid as a series of regular payments. :An annuity for which the payments are made at the end of each payment period.:An annuity for which the compounding and payment periods are the same. FUTURE VALUE OF AN ANNUITY:The future value of an annuity in which R is invested at the end of each of n regular intervals earning i of compound interest per interval is:365760071755FV = R = i = n = How did we get this? Think of a timeline of an annuity: Example 1: Chelsea plans to invest $1000 at the end of each 6-month period in an annuity that earns 4.8% compounded semi-annually for the next 20 years. a) Draw a timeline to represent this annuity. b) Determine the future value of his annuity after 20 years. Example 2: Joel needs $4000 to buy a new car in 2 years. He plans to make deposits into an account that earns 6.5% per year, compounded bi-weekly. a) Draw a timeline to represent this annuity. b) How much should she deposit bi-weekly? Example 3: Amir plans to invest $2600 each year at 6% per year, compounded annually, for the next 15 years. Compare the effects on the final amount if the deposits are made and compounding periods areAnnually c) MonthlyQuarterly d) WeeklyDo this on a separate sheet of paper if there is not enough room. ................
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