7.4 Annuities
Chapter
Chapter 7
Section
7.4
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Solutions 15 Videos

Calculate the amount of the annuity shown in the time line.

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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?

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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?

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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?

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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.

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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?

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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.

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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.
  • Follow his financial advisor?s suggestion about increasing the frequency of his deposits.
  • Switch to the competing bank.
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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?

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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?

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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.

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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.

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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.

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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.

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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

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Q18