Page 142 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, College Preparation
1. demonstrate an understanding of annuities, including mortgages, and solve related problems using technology;
2. gather, interpret, and compare information about owning or renting accommodation, and solve problems involving the associated costs;
3. design, justify, and adjust budgets for individuals and families described in case studies, and describe applications of the mathematics of personal finance.
1. Understanding Annuities
B. PERSONAL FINANCE OVERALL EXPECTATIONS
By the end of this course, students will:
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 gather and interpret information about annu- ities, describe the key features of an annuity, and identify real-world applications (e.g., RRSP, mortgage, RRIF, RESP)
1.2 determine, through investigation using tech- nology (e.g., the TVM Solver on a graphing calculator; online tools), the effects of chang- ing the conditions (i.e., the payments, the frequency of the payments, the interest rate, the compounding period) of an ordinary simple annuity (i.e., an annuity in which payments are made at the end of each period, and compounding and payment periods are the same) (e.g., long-term savings plans, loans)
Sample problem: Given an ordinary simple annuity with semi-annual deposits of $1000, earning 6% interest per year compounded semi-annually, over a 20-year term, which of the following results in the greatest return: doubling the payments, doubling the interest
rate, doubling the frequency of the payments and the compounding, or doubling the pay- ment and compounding period?
1.3 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
Sample problem: Using a spreadsheet, calcu- late the total interest paid over the life of a $10 000 loan with monthly repayments over 2 years at 8% per year compounded monthly, and compare the total interest with the origi- nal principal of the loan.
1.4 demonstrate, through investigation using technology (e.g., a TVM Solver), the advan- tages of starting deposits earlier when invest- ing in annuities used as long-term savings plans
Sample problem: If you want to have a mil- lion dollars at age 65, how much would you have to contribute monthly into an invest- ment that pays 7% per annum, compounded monthly, beginning at age 20? At age 35?
At age 50?
1.5 gather and interpret information about mort- gages, describe features associated with mortgages (e.g., mortgages are annuities for which the present value is the amount bor- rowed to purchase a home; the interest on a mortgage is compounded semi-annually but often paid monthly), and compare different types of mortgages (e.g., open mortgage, closed mortgage, variable-rate mortgage)
1.6 read and interpret an amortization table for a mortgage
Sample problem: You purchase a $200 000 condominium with a $25 000 down payment, and you mortgage the balance at 6.5% per year compounded semi-annually over 25 years,
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