At a glance
Solo · the culminating task of the money unit · working periods across the unit’s final classes · one plan in three parts, built on real rates
What you are making
This one is about your actual life. You will build a personal savings-and-borrowing plan with three parts, each powered by the mathematics of this unit:
- A goal. Something real — a car, a first apartment, a semester of tuition. Using compound interest, , work out what a single deposit today would grow to, and how long your goal takes at a rate you can actually find advertised.
- A habit. Nobody saves in one deposit. Design a regular-payment plan — an annuity — and show what it is worth at the end. Then change one condition at a time (payment size, frequency, rate) and report which change matters most.
- The mirror. Borrowing is the same mathematics pointed at you. Choose a realistic debt — a financed phone, a used car loan — and compute the total interest paid over its life. State, in one plain sentence, what the loan really costs beyond its sticker price.
The comparison table is the heart of the plan: scenarios side by side, so the reader can watch one condition change while everything else holds still — Money Over Time shows the pattern.
Milestones
- Goal chosen; a real advertised interest rate found and cited
- Part 1 computed two ways — formula and spreadsheet — and the two agree
- Part 2 scenarios tabled; the most powerful condition named
- Part 3 loan analysed; total interest stated next to the principal
- One page of plain-language advice written to your future self
How it is assessed
Per How Marks Work: reasoning, honesty, and communication — not the size of the imaginary fortune. A plan that concludes this loan is a bad idea is a strong plan. Your Math Journal entry — what surprised you most about the mirror — is part of the evidence, and Checking Your Own Work is the last step before handing it in.
Success criteria
| Quality | What it looks like in your plan |
|---|---|
| Real numbers | Rates are current, cited, and plausible |
| Two-way checks | Formula and spreadsheet agree, or the gap is explained |
| Fair comparisons | One condition changes at a time in the table |
| Honest debt | Total interest is stated plainly, next to the principal |
| Advice that lands | Your future self could act on the final page |
A word about the mirror
Advertising shows the payment, never the total. If your loan’s total interest surprises you, you have done the task correctly — write the surprise down. This is the one page from this course most worth keeping.
Curriculum connection
C3.3
solve problems, using a scientific calculator, that involve the calculation of the amount, (also referred to as future value, ), the principal, (also referred to as present value, ), or the interest rate per compounding period, , using the compound interest formula in the form [or ] Sample problem: Two investments are available, one at 6% compounded annually and the other at 6% compounded monthly. Investigate graphically the growth of each investment, and determine the interest earned from depositing $1000 in each investment for 10 years.
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C3.5
explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities (i.e., annuities in which payments are made at the end of each period, and compounding and payment periods are the same), geometric series, and exponential growth, through investigation with technology (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 ordinary simple annuity are related to the terms of a geometric series) 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?
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C3.6
determine, through investigation using technology (e.g., the TVM Solver on a graphing 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)
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C3.7
solve problems, using technology (e.g., scientific calculator, spreadsheet, graphing calculator), 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)
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