Question 1

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 2

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 3

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 4

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 5

A 20-year mortgage requires payments of $1,409.88 per month at an interest rate of 5.8% compounded monthly? What was the amount of the mortgage? What is the outstanding balance of the mortgage after 12 years?

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Question 6

Larissa plans to deposit $1,500 per year into a savings account paying 4.75% yearly for 10 years. She will leave the accumulated amount in the account for another 10 years at 5.25% compounded semi-annually. How much will Larissa have in the account after 20 years?

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Question 7

François and Pat wish to structure the payments from a 20-year annuity so that the end-of-quarter payments increase by $500 every five years. Maritime Insurance Co. will pay 5% compounded quarterly on funds received to purchase such an annuity. How much must François and Pat pay for an annuity in which the quarterly payments increase from $2,000 to $2,500 to $3,000 to $3,500 in successive five-year periods?

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Question 8

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 9

Kristina is deciding whether to deposit $1,000 per year for 10 years into an RRSP, or to wait five years, and then deposit $2,000 per year. If interest is 4.25% compounded yearly, which option should Kristina choose? What is the economic advantage of her choice?

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Question 10

For its "No Interest for One Year Sale," Flemming's Furniture advertises that customers pay only a 10% down payment. The balance may be paid by 12 equal monthly payments with no interest charges. Flemming's has an operating loan on which it pays interest at 8.4% compounded monthly. If Flemming's sells furniture in a cash transaction rather than on the 10%-down-and-no-interest promotion, Flemming's can use the extra cash proceeds to reduce the balance on its loan, and thereby save on interest costs. What percentage discount for cash could Flemming's give and still be no worse off than receiving full price under the terms of the sale?

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Question 11

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Question 12

You can purchase a residential building lot for $90,000 cash or for $20,000 down and quarterly payments of $5,000 for four years. The first payment would be due three months after the purchase date. If the money you would use for a cash purchase can earn 8% compounded quarterly during the next four years, which option should you choose? What is the economic advantage in current dollars of the preferred alternative?

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Question 13

Your client has the following choices for an insurance benefit: She can receive $2,000 at the end of each year for the next five years or one "lump" sum today. If the current interest rate is 4.5% compounded annually, what lump payment today is equivalent to the five payments? (Taken from CIFP course materials.)

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Question 14

A lottery offers the winner the choice between a $150,000 cash prize or month-end payments of $1,000 for 12½ years, increasing to $1,500 per month for the next 12½ years. Which alternative would you choose if money can earn 8.25% compounded monthly over the 25-year period?

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Question 15

Leona contributed $3,000 per year to her RRSP on every birthday from age 21 to age 30 inclusive. She stopped employment to raise a family and made no further contributions. Her husband, John, started to make annual contributions of $3,000 to his RRSP on his 31^st birthday and plans to continue up to and including his 65^th birthday. Assuming that both of their plans earn 8% compounded annually over the years, calculate and compare the amounts in their RRSPs at age 65.

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Question 16

Liam is investing $2,000 per year into his RRSP for five years at 3.5% compounded annually. Then he will add $1,500 every six months for the next five years at 3.75% compounded semi-annually. How much will Liam have in his account in total after 10 years?

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Question 17

Isaac wishes to purchase a 25-year annuity providing payments of $1000 at the end of each month for the first 15 years and $1500 at the end of each month for the remaining 10 years. If Isaac requires a minimum rate of return of 4.8% compounded monthly, what is the maximum price Isaac will be willing to pay for the annuity?

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Question 18

Sam has two offers to buy his is motorcycle. The first offer is a cash price of $15,000. The second offer is a down payment of $5,000, and quarterly payments of $725 for four years. If his money can earn 5.5% compounded quarterly, which option should Sam choose? What is the economic advantage?

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Question 19

An annuity contract pays $2,000 semi-annually for 15 years. What is the present value of the annuity six months before the first payment if money can earn 6% compounded semi-annually for the first six years and 10% compounded semi-annually for the next nine years?

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Question 20

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

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Quiz 10: Annuities: Future Value and Present Value

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

A 20-year mortgage requires payments of $1,409.88 per month at an interest rate of 5.8% compounded monthly? What was the amount of the mortgage? What is the outstanding balance of the mortgage after 12 years?

Larissa plans to deposit $1,500 per year into a savings account paying 4.75% yearly for 10 years. She will leave the accumulated amount in the account for another 10 years at 5.25% compounded semi-annually. How much will Larissa have in the account after 20 years?

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

Kristina is deciding whether to deposit $1,000 per year for 10 years into an RRSP, or to wait five years, and then deposit $2,000 per year. If interest is 4.25% compounded yearly, which option should Kristina choose? What is the economic advantage of her choice?

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):

A lottery offers the winner the choice between a $150,000 cash prize or month-end payments of $1,000 for 12½ years, increasing to $1,500 per month for the next 12½ years. Which alternative would you choose if money can earn 8.25% compounded monthly over the 25-year period?

Liam is investing $2,000 per year into his RRSP for five years at 3.5% compounded annually. Then he will add $1,500 every six months for the next five years at 3.75% compounded semi-annually. How much will Liam have in his account in total after 10 years?

Sam has two offers to buy his is motorcycle. The first offer is a cash price of $15,000. The second offer is a down payment of $5,000, and quarterly payments of $725 for four years. If his money can earn 5.5% compounded quarterly, which option should Sam choose? What is the economic advantage?

An annuity contract pays $2,000 semi-annually for 15 years. What is the present value of the annuity six months before the first payment if money can earn 6% compounded semi-annually for the first six years and 10% compounded semi-annually for the next nine years?

Calculate the periodic interest rate that matches the payment interval for each annuity (to the nearest 0.001%):