MCR3U.1 Financial Applications of Sequences and Series

• MCR3U.1.a solve problems involving arithmetic and geometric sequences and series;

• MCR3U.1.b solve problems involving compound interest and annuities;

• MCR3U.1.b solve problems involving financial decision making, using spreadsheets or other appropriate technology.

Specific Expectations

MCR3U.1.1 Solving Problems Involving Arithmetic and Geometric Sequences and Series

By the end of this course, students will:

• MCR3U.1.1.a write terms of a sequence, given the formula for the nth term or given a recursion formula;
• MCR3U.1.1.b determine a formula for the nth term of a given sequence (e.g., the nth term of the sequence , , , . . . is );
• MCR3U.1.1.c identify sequences as arithmetic or geometric, or neither;
• MCR3U.1.1.d determine the value of any term in an arithmetic or a geometric sequence, using the formula for the nth term of the sequence;
• MCR3U.1.1.e determine the sum of the terms of an arithmetic or a geometric series, using appropriate formulas and techniques.

MCR3U4U.1.2 Solving Problems Involving Financial Decision Making

By the end of this course, students will:

• MCR3U.1.2.a analyse the effects of changing the conditions in long-term savings plans (e.g., altering the frequency of deposits, the amount of deposit, the interest rate, the compounding period, or a combination of these) (Sample problem: Compare the results of making an annual deposit of $1000 to an RRSP, beginning at age 20, with the results of making an annual deposit of $3000, beginning at age 50);
• MCR3U.1.2.b describe the manner in which interest is calculated on a mortgage (i.e., compounded semi-annually but calculated monthly) and compare this with the method of interest compounded monthly and calculated monthly;
• MCR3U.1.2.c generate amortization tables for mortgages, using spreadsheets or other appropriate software;
• MCR3U.1.2.d analyse the effects of changing the conditions of a mortgage (e.g., the effect on the length of time needed to pay off the mortgage of changing the payment frequency or the interest rate);
• MCR3U.1.2.e communicate the solutions to problems and the findings of investigations with clarity and justification.