7.4 Annuities
Chapter
Chapter 7
Section
7.4
Solutions 15 Videos

Calculate the amount of the annuity shown in the time line. 0.42mins
Q1

To help her granddaughter with university costs, Sasha's grandmother puts $250 into an account that earns 4.5% per year, compounded annually, at the end of every year for 6 years. (a) Draw a time line to represent this annuity. (b) Determine the amount of the annuity. (c) How much interest was earned? Buy to View 2.02mins Q2 How much must be invested at the end of each year, for 4 years, to achieve an amount of \$10 000, if interest is earned at a rate of 6.25% per year, compounded annually?

1.30mins
Q4

Lucy wants to have \$18 000 in her account 3 years from now to buy a car. How much must she invest per month, if her account earns 7.2\% annual interest, compounded monthly? Buy to View 3.00mins Q5 Donna invests \$75 every 2 weeks in an account that earns compound interest bi-weekly. If she does this for 7 years, she will end up with \$16 939.83 in the account. (a) How much total interest will have been earned? (b) Determine the annual rate of interest, compounded bi-weekly. Buy to View 4.50mins Q6 Matt is planning to deposit \$160 per month into an account that earns 4.8% annual interest, compounded monthly, for 15 years.

(a) Determine the amount in the account at the end of this annuity.

(b) How much interest will have been earned?

3.35mins
Q8

Matt is planning to deposit \$160 per month into an account that earns 4.8% annual interest, compounded monthly, for 15 years. Maurice's financial advisor suggests that he would improve the value of his annuity if he changed his payments to \$40 per week, at the same interest rate, compounded weekly. Do you agree or disagree with the financial advisor? Justify your response with mathematical reasoning.

2.04mins
Q9

Matt is planning to deposit \$160 per month into an account that earns 4.8% annual interest, compounded monthly, for 15 years. A competing bank offers Maurice 5% per annum, compounded monthly, for his monthly deposits of \$160. Which option should Maurice choose? Justify your answer with mathematical reasoning.

• Stick with his current arrangement.
• Switch to the competing bank.
1.11mins
Q10

Lee would like to retire at age 60 and is considering two investment options:

Option A: Invest \$500 per month beginning at age 20. Option B: Invest \$1000 per month beginning at age 40.

In both cases, the interest is 6\% per annum, compounded monthly. Which option pays more interest, and by how much?

3.44mins
Q11

Peter wants to be a millionaire before he retires. He plans to save a certain amount every week for 40 years.

If he puts money in an investment that earns 7% annual interest, compounded weekly, what amount must Peter deposit weekly?

3.54mins
Q12

 \displaystyle A = \frac{100(1.05^n - 1)}{0.05}  represents the amount of an annuity.

Write a function to describe the total principal invested after n compounding periods.

0.14mins
Q14a

Bethany starts investing $300 per month at 6% per annum, compounded monthly, for 5 years. After 3 years, the interest increases to 9% per annum, compounded monthly. Determine the amount of her investment after 5 years. The end of the period of 5 years is when Bethany deposits her final$300.

Q15

In \triangle ABC, a = 10 mm, b = 26 mm, and c = 24 mm. If D is the midpoint of AC and BC is extended to E such that DE = 24 mm, determine the measure of \angle CED without using a calculator.

Q16

Given that a^2 + (a + b)^2 = 100 and a and b are whole numbers, determine all possible ordered pairs (a, b) that solve this equation.

Q17

Given x^2 - y^2= 2311, 2311 = (2)(3)(5)(7)(11) + 1, and x > y > 0, where x and y are integers, which of the following is true?

A. only x is divisible by 11

B. only y is divisible by 11

C. both are divisible by 11

D. neither is divisible by 11