8.5 Present Value
Chapter
Chapter 8
Section
8.5
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Lecture on Present Value of Annuity 3 Videos
Solutions 27 Videos

Each situation represents a loan.

  • i) Draw a timeline to represent the amount of the original loan.
  • ii) Write the series that represents the amount of the original loan.
  • iii) Calculate the amount of the original loan.
  • iv) Calculate the interest paid.

Regular Payment: \$650 per year

Rate of Compound Interest per Year: \$3.7\% per year

Compounding Period: annually

Time: 5 yeas

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2.39mins
Q1a

Each situation represents a loan.

  • i) Draw a timeline to represent the amount of the original loan.
  • ii) Write the series that represents the amount of the original loan.
  • iii) Calculate the amount of the original loan.
  • iv) Calculate the interest paid.

Regular Payment: \$1200 every 6 months

Rate of Compound Interest per Year: \$9.4\% per year

Compounding Period: semi-annually

Time: 9 years

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2.15mins
Q1b

Each situation represents a loan.

  • i) Draw a timeline to represent the amount of the original loan.
  • ii) Write the series that represents the amount of the original loan.
  • iii) Calculate the amount of the original loan.
  • iv) Calculate the interest paid.

Regular Payment: \$84.73 per quarter

Rate of Compound Interest per Year: \$3.6\% per year

Compounding Period: quarterly

Time: 3\dfrac{1}{2} years

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1.58mins
Q1c

Each situation represents a loan.

  • i) Draw a timeline to represent the amount of the original loan.
  • ii) Write the series that represents the amount of the original loan.
  • iii) Calculate the amount of the original loan.
  • iv) Calculate the interest paid.

Regular Payment: \$183.17 per quarter

Rate of Compound Interest per Year: \$6.6\% per year

Compounding Period: monthly

Time: 10 years

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1.33mins
Q1d

Each situation represents a simple, ordinary annuity.

  • i) Calculate the present value of each payment.
  • ii) Write the present values of the payments as a series.
  • iii) Calculate the present value of the annuity.

Regular Payment: \$800 per quarter

Rate of Compound Interest per Year: \$9\% per year

Compounding Period: annually

Time: 7 years

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1.32mins
Q2a

Each situation represents a simple, ordinary annuity.

  • i) Calculate the present value of each payment.
  • ii) Write the present values of the payments as a series.
  • iii) Calculate the present value of the annuity.

Regular Payment: \$300 every 6 months

Rate of Compound Interest per Year: \$8\% per year

Compounding Period: semi-annually

Time: 3.5 years

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1.13mins
Q2b

Each situation represents a simple, ordinary annuity.

  • i) Calculate the present value of each payment.
  • ii) Write the present values of the payments as a series.
  • iii) Calculate the present value of the annuity.

Regular Payment: \$750 every 6 months

Rate of Compound Interest per Year: \$8\% per year

Compounding Period: quarterly

Time: 2 years

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1.23mins
Q2c

Calculate the present value of each annuity.

Regular Payment: \$5000 per year

Rate of Compound Interest per Year: \$7.2\% per year

Compounding Period: annually

Time: 5 years

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0.44mins
Q3a

Calculate the present value of each annuity.

Regular Payment: \$250 per year

Rate of Compound Interest per Year: \$4.8\% per year

Compounding Period: semi-annually

Time: 12 years

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0.46mins
Q3b

Calculate the present value of each annuity.

Regular Payment: \$25.50 per week

Rate of Compound Interest per Year: \$5.2\% per year

Compounding Period: weekly

Time: 100 weeks

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0.44mins
Q3c

Calculate the present value of each annuity.

Regular Payment: \$48.50 per week

Rate of Compound Interest per Year: \$23.4\% per year

Compounding Period: monthly

Time: 2\frac{1}{2}

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Q3d

You want to buy a \$1300 stereo on credit and make monthly payments over 2 years. If the store is charging you 18\%/a compounded monthly, what will be your monthly payments?

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2.06mins
Q4

Lori wants to buy a snowmobile. She can borrow $7500 at 10%/a compounded quarterly if she repays the loan by making equal quarterly payments for 4 years.

a) Draw a timeline to represent the annuity.

b) Write the series that represents the present value of the annuity.

c) Calculate the quarterly payment that Lily must make.

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2.17mins
Q5

Ron pays $50 for a DVD/CD player and borrows the remaining amount. He plans to make 10 monthly payments of \$40 each. The first payment is due next month.

a) The interest rate is 18\%/a compounded monthly. What was the selling price of the player?

b) How much interest will he have paid over the term of the loan?

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2.08mins
Q6

Elle is investing \$128 000 at 7.8\%/a compounded monthly. She wants to withdraw an equal amount from this investment each month for the next 25 years as spending money. What is the most she can take out each month?

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2.15mins
Q7

The Peter's family wants to buy a cottage for \$69 000. Paul can pay \$5000 and finance the remaining amount with a loan at 9\%/a compounded monthly. The loan payments are monthly, and they may choose either a 7-year or a 10-year term.

  • Calculate the monthly payment for each term.
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2.32mins
Q8a

The Peter's family wants to buy a cottage for \$69 000. Paul can pay \$5000 and finance the remaining amount with a loan at 9\%/a compounded monthly. The loan payments are monthly, and they may choose either a 7-year or a 10-year term.

  • i. How much would they save in interest by choosing the shorter term?

  • ii. What other factors should the Paul consider before making their financing decision?

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2.06mins
Q8bc

Charles would like to buy a new car that costs \$32 000.

  • The dealership offers to finance the car at 2.4%/a compounded monthly for five years with monthly payments.
  • The dealer will reduce the selling price by \$3000 if Charles pays cash. Charles can get a loan from his bank at 5.4%/a compounded monthly and paid in cash.

Which is the best way to buy the car? Justify your answer with calculations.

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4.44mins
Q9

To pay off $35 000 in loans, Nina’s bank offers her a rate of 8.4%/a compounded monthly. She has a choice between a 5-, 10-, or 15-year term.

Determine the monthly payment for each term.

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2.44mins
Q10a

To pay off $35 000 in loans, Nina’s bank offers her a rate of 8.4%/a compounded monthly. She has a choice between a 5-, 10-, or 15-year term.

Calculate how much interest Nina would pay in each case.

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1.19mins
Q10b

Pedro pays $45 for a portable stereo and borrows the remaining amount. The loan payments are $25 per month for 1 year. The interest rate is 18.6%/a compounded monthly.

What was the selling price of the stereo?

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2.09mins
Q11a

Pedro pays $45 for a portable stereo and borrows the remaining amount. The loan payments are $25 per month for 1 year. The interest rate is 18.6%/a compounded monthly.

How much interest will Pedro have paid over the term of the loan?

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0.26mins
Q11b

Susan buys a new computer for $2500. She pays $700 and finances the rest at $75.84 per month for 2.5 years. What annual interest rate, compounded monthly, is Susan being charged? Round your answer to two decimal places.

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5.01mins
Q12

Leo invests $50 000 at 11.2%/a compounded quarterly for his retirement. Leo’s financial advisor tells him that he should take out a regular amount quarterly when he retires. If Leo has 20 years until he retires and wants to use the investment for recreation for the first 10 years of retirement, what is the maximum quarterly withdrawal he can make?

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3.29mins
Q13

Cass calculates that she will require about $2500 per month for the first 15 years of her retirement. If she has 25 years until she retires, how much should she invest each month at 9%/a compounded monthly for the next 25 years if she plans to withdraw $2500 per month for the 15 years after that?

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3.59mins
Q14

A lottery has two options for winners collecting their prize:

  • Option A: \$1000 each week for life

  • Option B: \$660 000 in one lump sum

The current interest rate is 6.76%/a compounded weekly.

a) Which option would you suggest to a winner who expects to live for another 25 years?

b) When is option A better than option B?

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4.49mins
Q15

Carol must repay student loans that total \$17\ 000. She can afford to make \$325 monthly payments. The bank is charging an interest rate of 7.2\%/a compounded monthly. How long will it take Carol to repay her loans?

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2.57mins
Q18