Page 54 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

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THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
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3.5 explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities (i.e., annuities in which pay- ments are made at the end of each period, and compounding and payment periods are the same), geometric series, and exponential growth, through investigation with techno- logy (e.g., use a spreadsheet to determine and graph the future value of an ordinary simple annuity for varying numbers of compounding periods; investigate how the contributions of each payment to the future value of an ordi- nary simple annuity are related to the terms of a geometric series)
3.6 determine, through investigation using technology (e.g., the TVM Solver on a graph- ing calculator, online tools), the effects of changing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of ordinary simple annuities (e.g., long-term savings plans, loans)
Sample problem: Compare the amounts at age 65 that would result from making an annual deposit of $1000 starting at age 20, or from making an annual deposit of $3000 starting at age 50, to an RRSP that earns 6% interest per annum, compounded annually. What is the total of the deposits in each situation?
3.7 solve problems, using technology (e.g., scien- tific calculator, spreadsheet, graphing calcula- tor), that involve the amount, the present value, and the regular payment of an ordinary simple annuity (e.g., calculate the total interest paid over the life of a loan, using a spreadsheet, and compare the total interest with the original principal of the loan)