Deck 12: Annuities: Special Situations

Question 1

Hard Rock Paving Company is applying for a loan. It is your job to determine how much they will be able to borrow. They will not be making any payments for the first 15 months. After that, they will make payments of $1,000 per month for four years. There is no interest-free grace period. The first $1,000 payment will be made 15 months after the loan is received. If the interest rate is 13.2% compounded monthly, how much can they expect to borrow?

A) $37,138
B) $31,864
C) $31,517
D) $33,915
E) $40,736

Answer 1

$31,864

Question 2

Heather is planning to retire in 10 years. She will then need an income of $1,500 at the end of every month for the subsequent 25 years. She is going to make one investment today to provide all of the money she will eventually collect. Her investments will earn 12% compounded monthly. How much should she invest today?

A) $43,152.46
B) $67,449.00
C) $92,461.46
D) $139,437.52
E) $167,687.74

Answer 2

$43,152.46

Question 3

What is the economic value today of 24 monthly payments of $500 with the first payment occurring 10 months from today? Assume that money can earn 12% compounded monthly.

A) $9,711.84
B) $8,973.34
C) $10,621.69
D) $9,615.68
E) $13,486.73

Answer 3

$9,711.84

Question 4

Calculate the present value of a deferred annuity of 20 annual payments of $100,000 each The interest rate is 13.5% compounded annually and the first payment will be made 11 years from now.

A) $169,340
B) $593,451
C) $218,148
D) $681,890
E) $192,201

Question 5

Fred intends to retire in 10 years. To supplement his pension, he would like to receive $500 every six months for 20 years. If he is to receive the first payment six months after the date of his retirement, what lump amount must he invest today to achieve his goal? Assume that the investment will earn 12% compounded semi-annually.

A) $2,486.50
B) $4,871.78
C) $5,164.09
D) $2,345.75
E) $2,212.97

Question 6

Harold is planning to retire in 21 years. After that he will need an income of $4,500 at the end of every month for the subsequent 25 years. He is going to make one investment today to provide all of the money he will eventually collect. His investments will earn 9% compounded monthly. How much should he invest today?

A) $103,817
B) $104,397
C) $81,582
D) $82,194
E) $205,390

Question 7

Mrs. O'Halloran gave $130,000 to the University of Northern British Columbia for a perpetual scholarship fund. What amount can be awarded on each anniversary if the scholarship fund earns 7% compounded annually?

A) $13,000
B) $1,300
C) $1,857
D) $9,100
E) $91,000

Question 8

Andy deposits $40,000 into an account earning 6.6% compounded annually for 5 years. After this time, Andy wishes to withdraw $2,814.41 at the end of each quarter and have $10,000 remaining. Determine the number of withdrawals Andy can make.

A) 20 withdrawals
B) 24 withdrawals
C) 28 withdrawals
D) 32 withdrawals
E) 36 withdrawals

Question 9

An individual wants to receive end-of-month payments of $1,200 for 20 years after she retires 15 years from now. What lump amount must she invest today to provide the retirement income? Assume the investment earns 7% compounded monthly for the entire 35 years.

A) $49,864.93
B) $54,645.42
C) $54,328.50
D) $187,835.65
E) $155,681.89

Question 10

Gregory deposits a $30,000 for a period of time at a 3.5% rate of interest compounded semi-annually. The accumulated amount provides Gregory the benefit of withdrawing $1,165 at the end of each month for three years. Determine how long the initial deposit accumulated interest.

A) 3 years
B) 4 years
C) 5 years
D) 6 years
E) 7 years

Question 11

Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, what is the amount that Moses will be able to take out of his Retirement Fund at the end of every six months for 25 years after he retires?

A) $17,053
B) $24,270
C) $28,984
D) $3,053
E) $6,324

Question 12

Calculate the present value of a deferred annuity of 20 annual payments of $25,000 each The interest rate is 8.5% compounded annually and the first payment will be made in six years.

A) $306,472
B) $211,760
C) $157,339
D) $145,013
E) $104,289

Question 13

What amount can be paid at the end of every month in perpetuity from an endowment of $350,000 which is earning 5.4% compounded monthly?

A) $1,575
B) $1,890
C) $2,100
D) $15,750
E) $18,900

Question 14

A purchase agreement for a $22,000 truck requires 60 equal payments every six months. If the first payment is due one year after the date of purchase and interest is charged at 18% compounded monthly, what is the size of each payment?

A) $2,065.46
B) $1,888.95
C) $1,991.31
D) $2,469.50
E) $2,258.47

Question 15

Anita is planning to go back to school in 2 years. Once at school, she wishes to be able to withdraw $900 at the end of each month for 2 years. If interest is 4.5% compounded monthly, determine the amount that should be deposited now to fulfil her goal.

A) $18,848.06
B) $19,675.25
C) $20,437.43
D) $20,884.13
E) $21,973.28

Question 16

Fred purchased a farm with a down payment of $8,500 and 48 semi-annual payments of $3,000. The first of these payments is to be made two years after the date of purchase. What was the purchase price of the farm if the interest rate charged on the balance is 14% compounded semi-annually?

A) $41,191.42
B) $31,424.74
C) $42,124.47
D) $39,924.74
E) $49,691.42

Question 17

The Pithybottoms want to make a donation to set up a scholarship trust fund at Hinose College. The fund is to support payments of $5,000 at the end of every three months in perpetuity. If the fund earns 7.5% compounded quarterly, how much must they donate?

A) $666,667
B) $375,000
C) $266,667
D) $66,667
E) $200,000

Question 18

What amount can be paid at the end of every month, in perpetuity, from an endowment of $75,000 earning 8% compounded monthly?

A) $800
B) $750
C) $500
D) $400
E) $250

Question 19

Harry deposits $10,000 into an investment account that earns 7% compounded monthly. How many monthly withdrawals of $310 will he be able to make if his first withdrawal is exactly five years after his deposit?

A) 36
B) 40
C) 54
D) 41
E) 53

Question 20

Evergreen Landscaping is applying for a loan. Your help is needed to determine how much they can borrow. They will not be able to make any payments for the first 18 months. After that, they will make payments of $750 per month for five years. There is no interest-free grace period. The first $750 payment will be made 18 months after the loan is received. If the interest rate is 10.5% compounded monthly, how much can they expect to borrow?

A) $29,829
B) $34,894
C) $36,515
D) $30,090
E) $24,008

Question 21

If a donation of $100,000 is expected to pay out scholarships of $10,000 every year and the funds earn 7.5% compounded annually, how long will it be before the first annual payment can be made?

A) 3 years
B) 5 years
C) 7 years
D) 9 years
E) 11 years

Question 22

What amount, invested today at 5% compounded quarterly, will support perpetual monthly payments of $800? The first payment will be made one month from now.

A) $116,327
B) $192,798
C) $160,000
D) $63,997
E) $322,700

Question 23

The National Museum has received a donation of $2,000,000 which is to be used to purchase new exhibits at the end of every three months. If the money earns 12% compounded annually, how much could be paid out every three months in perpetuity?

A) $60,000
B) $57,475
C) $24,000
D) $114,704
E) $72,895

Question 24

Simon Fraser recently received a $20 million donation to be used for scholarship purposes. If interest can be earned at 4.2% compounded monthly, determine the semi-annual amount of scholarships that students can apply for.

A) $423,692.20
B) $428,550.12
C) $431,084.45
D) $441,289.72
E) $444,821.94

Question 25

A wealthy benefactor has donated $1,000,000 to establish a perpetuity that is to pay a constant payment once per month. The money will earn 10% compounded annually. The first monthly perpetual payment will be made 28 months from now. Determine the size of the payments.

A) $9,960
B) $10,000
C) $9,881
D) $8,603
E) $10,047

Question 26

A trust fund of $55,000 is invested at 8.4% compounded monthly. It is to be left to accumulate interest for five years after which it is to support, in perpetuity, equal payments to be made at the end of every month. What will be the size of the payments?

A) $385
B) $585
C) $741
D) $916
E) $1,126

Question 27

A donation of $250,000 is made today to the local library for the purchase of new books. What amount can be withdrawn every month in perpetuity if the money is earning 9% compounded monthly and the first payment is to be made immediately?

A) $2,250.00
B) $1,875.00
C) $1,861.04
D) $1575.00
E) $1562.77

Question 28

What amount can be paid at the end of every six months, in perpetuity, from an endowment of $475,000 earning 7% compounded annually?

A) $16,625
B) $16,344
C) $15,682
D) $14,971
E) $11,579

Question 29

A local college provides annual scholarships totalling $5,000 to business students. If interest is at 3.1% compounded quarterly, determine the original amount that was deposited.

A) $153,282.84
B) $156,857.13
C) $159,427.39
D) $160,834.67
E) $161,349.04

Question 30

What is the present value of a trust fund that earns 8.8% compounded annually and pays out $3,500 every three months? The next payment is due to be made today.

A) $164,249
B) $745,820
C) $167,749
D) $529,722
E) $526,222

Question 31

A wealthy donor made a $50,000 contribution to a local charity. The charity invested this amount for three years at an interest rate of 2.4% compounded annually. At the end of this time, the charity wished to provide monthly benefits in perpetuity to those in need. Determine the amount that the charity can provide on a monthly basis.

A) $125.12
B) $114.74
C) $108.66
D) $106.21
E) $103.90

Question 32

What amount, invested today at 6% compounded monthly, will support perpetual monthly payments of $500? The first payment will be made one month from now.

A) $500,000
B) $400,000
C) $300,000
D) $200,000
E) $100,000

Question 33

The Willie P. Stanton Trust Fund is to pay, $5,000 at the end of every year to the student-athlete voted most deserving based on his or her dedication to the ideals of good citizenship. The Trust Fund earns 7.4% compounded semi-annually. What is the present value of this perpetuity?

A) $66,340
B) $129,526
C) $72,341
D) $135,135
E) $67,568

Question 34

Calculate the present value of a perpetuity that will pay out $1,500 every month and the first payment is to be made 10 years from now. The interest rate earned is 9% compounded annually.

A) $81,587
B) $82,199
C) $92,761
D) $88,546
E) $87,913

Question 35

An endowment fund of $5,000,000 is to pay out grants for medical research. The grants are to be paid once per month and the first one is to be paid today. The fund will earn interest at 11% compounded semi-annually. What is the size of the monthly grants?

A) $45,833
B) $27,500
C) $39,782
D) $44,419
E) $44,817

Question 36

Calculate the present value of a perpetuity that will pay out $7,500 every six months. The first payment will be made four years from now. The interest rate earned is 8.6% compounded semi-annually.

A) $174,419
B) $129,898
C) $124,543
D) $119,563
E) $104,826

Question 37

You wish to donate $10,000 to a local charity in order for it to provide annual benefits of $750 per year in perpetuity. If interest is compounded monthly, determine the interest rate needed to fulfil this goal.

A) 8.25%
B) 8.00%
C) 7.75%
D) 7.50%
E) 7.25%

Question 38

What is the present value of a trust fund that earns 9% compounded monthly and pays out $950 every month into perpetuity? The next payment will be made today.

A) $126,667
B) $105,556
C) $141,667
D) $127,617
E) $95,950

Question 39

If an endowment fund of $2,327,000 is to be used to pay out grants of $175,000 at the end of every year in perpetuity what effective rate of interest must the funds earn?

A) 11.61%
B) 10.06%
C) 8.93%
D) 7.52%
E) 5.44%

Question 40

A $450,000 trust fund earns 8% compounded semi-annually. It is to make perpetual payments at the end of every month. What will be the size of the monthly payments?

A) $3,000
B) $1,800
C) $1,955
D) $2,453
E) $2,951

Question 41

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

Question 42

Mary needs a pension that will pay her $12,000 one year from now and annual payments for 24 more years that are each 5% larger than the previous year. If the funds in her Retirement Fund earn 7.5% compounded annually, how much money must she have there now?

A) $188,490
B) $266,540
C) $532,842
D) $213,460
E) $487,671

Question 43

An 18-year-old college student plans to save a "Buck-A-Day" in a glass jar and after one year, set up a Retirement Savings Plan with $365. One year later he will make his second contribution to the RSP but it will be 10% larger than the first one. He will continue to increase his annual contributions by 10%. He anticipates that his investments can earn an annual return of 12.5% compounded annually. How much money is he expecting to have in the RSP after 40 years?

A) $773,510
B) $1,529,444
C) $1,411,823
D) $962,720
E) $284,291

Question 44

A loan of $126,500,000 is to be repaid by annual payments for 25 years. The payments will form a constant growth annuity with each payment being 20% larger than the previous one. The interest rate charged on the loan is 11% compounded annually. What is the size of the first payment?

A) $1,890,589
B) $2,729,835
C) $5,060,000
D) $9,756,417
E) $15,020,641

Question 45

We will make annual RRSP contributions at the end of every year for 35 years and each contribution is going to be 8% larger than the previous one. Our goal is to have $2,000,000 in 35 years. The RRSP will earn 13% compounded annually. How large will the first contribution be?

A) $1,048
B) $1,483
C) $1,746
D) $2,295
E) $3,742

Question 46

What amount of money invested now will provide monthly payments of $200 for five years, if the ordinary annuity is deferred for 3½ years and the money earns 3.75% compounded monthly?

Question 47

Christian plans to initially contribute $3,000 and increase his yearly contributions by 5% each year for 20 years. If the rate of interest is 7% compounded annually, determine the amount of his payment in year 12.

A) $5,387.56
B) $5,687.56
C) $5,987.56
D) $6,287.56
E) $6,587.56

Question 48

Marion's grandfather will establish a trust that will pay her $1,500 every three months for 11 years. The first payment will be made six years from now, when she turns 19. If money is worth 6.5% compounded quarterly, what is today's economic value of the bequest?

Question 49

We are aiming to have $5,000,000 in 45 years and we plan to get there by making monthly investments that are 1% larger than the previous month's investment. Our funds will earn 14.4% compounded monthly. How much should be invested at the end of the first month?

A) $24.29
B) $68.82
C) $103.74
D) $425.16
E) $801.93

Question 50

Barklay has $782,490 in his Retirement Saving Plan and he wants to start receiving income at the end of every three months for the next 22 years. The funds earn 7% compounded quarterly and he wants each payment that he receives to be 1.5% larger than the previous one. How much will the first payment be three months from now?

A) $2,675
B) $6,429
C) $10,050
D) $15,829
E) $17,767

Question 51

Using an inheritance he recently received, Sam wants to purchase a deferred annuity that will pay $5,000 every three months between age 60 (when he plans to retire) and age 65 (when his permanent pension will begin). The first payment will be received three months after he reaches 60, and the last payment will be received on his 65^th birthday. If Sam's current age is 50 years and 6 months and the invested funds will earn 4.4% compounded quarterly, what amount must he invest in the deferred annuity?

Question 52

An investment of $50 is to be made at the end of this month and that amount is increased by 1% every month for 40 years. The investments are expected to earn 13.2% compounded monthly. What should be the total value of these investments in 40 years?

A) $3,607,093
B) $862,680
C) $1,847,397
D) $997,481
E) $2,646,194

Question 53

How much money would accumulate over 35 years if the investor makes an investment of $3,500 at the end of the first year and always increases the size of the annual investment by 5% over the previous year. The investments are expected to earn 11% compounded annually.

A) $1,195,563
B) $1,928,432
C) $1,010,619
D) $1,624,915
E) $2,311,587

Question 54

Edward wishes to have $450,000 in his retirement plans in 25 years. He plans to make annual contributions that will increase by 1% each year. If interest is earned at 5% compounded annually, determine the value of the initial payment in year 1.

A) $6,555.45
B) $7,005.45
C) $7,555.45
D) $8.005.45
E) $8,555.45

Question 55

What amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 5.4% compounded monthly.

Question 56

Nino plans to initially contribute $10,000 and increase his yearly contributions by 2% each year for 15 years. If the rate of interest is 4% compounded annually, determine how much the investment will be worth in 15 years.

A) $227,537.58
B) $229,537.58
C) $231,537.58
D) $233,537.58
E) $235,537.58

Question 57

Baba Lou plans to retire in 20 years. At that point, he plans to collect payments at the end of every six months that are 2% larger than the previous payment, and this is to continue for 30 years. The first payment will be $16,500. His retirement plan is expected to earn 7% compounded semi-annually after he retires and 10% compounded annually before he retires. What single investment should he make now to fund the whole retirement plan?

A) $68,590
B) $95,411
C) $241,917
D) $316,443
E) $641,877

Question 58

How much will it cost to purchase a 20-year indexed annuity in which the end of quarter payments start at $6,000 and grow by 0.5% every quarter? Assume that the money used to purchase the annuity earns 8% compounded quarterly.

A) $277,727
B) $480,000
C) $316,842
D) $516,667
E) $326,744

Question 59

Mr. Haddit plans to retire eight years from today. He projects that he will need $30,000 per year in his retirement which he assumes will be for 15 years. The first payment will be nine years from today. To fund his retirement, Mr. Haddit will invest a lump amount today and later use it to sustain the 15 withdrawals. If his investment earns 6% compounded annually, how much must he invest today?

Question 60

Calculate the present value of a 25-year annuity making semi-annual payments that grow at a rate of 4% compounded annually. The first payment is $25,000 and the funds earn 8% compounded semi-annually.

A) $606,574.51
B) $676,574.51
C) $706,574.51
D) $776,574.51
E) $876,574.51

Question 61

A perpetuity is to pay $10,000 at the end of every six months. How much less money is required to fund the perpetuity if the money can be invested to earn 5% compounded semi-annually?

Question 62

$10,000 was invested in a fund earning 7.5% compounded monthly. How many monthly withdrawals of $300 can be made if the first occurs 3½ years after the date of the initial investment? Count the final smaller withdrawal.

Question 63

Mrs. Corriveau has just retired at age 58 with $299,317 in her RRSP. She plans to live off other savings for a few years and allow her RRSP to continue to grow on a tax-deferred basis until there is a sufficient amount to purchase a 25-year annuity paying $2,000 at the end of each month. If her RRSP and the annuity each earn 3.75% compounded monthly, how much longer must she let her RRSP grow (before she buys the annuity)?

Question 64

How much more money is required to fund an ordinary perpetuity than a 30-year ordinary annuity if both pay $5,000 quarterly and money can earn 5% compounded quarterly?

Question 65

Mr. Donatelli moved from Toronto to Winnipeg to take a job promotion. After selling their Toronto home and buying a home in Winnipeg, the Donatellis have $85,000 in cash on hand. If the funds are used to purchase a deferred annuity from a life insurance company providing a rate of return of 8.25% compounded annually, what payments will they receive at the end of every six months for 20 years after a 9-year deferral period?

Question 66

Mrs. O'Reilly donated $500,000 to Medicine Hat College for a perpetual scholarship fund for women in business studies. What amount can be awarded on each anniversary if the scholarship fund earns 4½% compounded annually?

Question 67

During a one-week promotion, Al's Appliance Warehouse is planning to offer terms of "nothing down and nothing to pay for four months" on major appliances priced above $500. Four months after the date of sale, the first of eight equal monthly payments is due. If the customer is to pay interest at the rate of 12% compounded monthly on the outstanding balance from the date of sale, what will be the monthly payments on an automatic dishwasher priced at $995?

Question 68

Nancy borrowed $8,000 from her grandfather to buy a car when she started college. The interest rate being charged is only 4.5% compounded monthly. Nancy is to make the first $200 monthly payment on the loan three years after the date of the loan. How long after the date of the initial loan will she make the final payment?

Question 69

A $20,000 investment will be allowed to grow at 4.5% compounded semi-annually until it can support semi-annual withdrawals of $1,000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

Question 70

An old agreement requires a town to pay $500 per year in perpetuity to the owner of a parcel of land for a water-well dug on the property in the 1920s. The well is no longer used, and the town wants to buy out the contract, which has become an administrative nuisance. What amount (including the regular scheduled payment) should the landowner be willing to accept on the date of the next scheduled payment if long-term low-risk investments now earn 3.8% compounded annually?

Question 71

A property development company obtained a $2.5 million loan to construct a commercial building. The interest rate on the loan is 5% compounded semi-annually. The lender granted a period of deferral until rental revenues become established. The first quarterly payment of $100,000 is required 21 months after the date of the loan. How long after the date of the original loan will the last payment be made?

Question 72

Negotiations between Delco Manufacturing and the union representing its employees are at an impasse. The union is seeking a 4.5% wage increase. Delco's offer is 2%. The employees have passed a vote authorizing job action. Suppose the union succeeds in winning the 4.5% increase after a two-month strike. For an employee 10 years from retirement, will there be any economic gain? Compare the current economic values of (1) 10 years' end-of-month wages at the employer's offer (102% of last year's wages) vs. (2) wages including a 4.5% increase to the same horizon but after a two-month strike. Assume money is worth 6% compounded monthly.

Question 73

How long is the period deferral if the first quarterly payment of a deferred annuity will be paid 3½ years from today?

Question 74

Ranger Oil recently donated $750,000 to the Northern Alberta Institute of Technology (NAIT) to fund (in perpetuity) five annual bursaries for students in Petroleum Engineering Technology. If the first five bursaries are to be awarded immediately, what is the maximum amount of each bursary? Assume that the bursary fund earns 4.9% compounded semi-annually.

Question 75

Mr. O'Connor set up a trust account paying $500 per month in perpetuity to the local hospital. These payments consume all the interest earned monthly by the trust. Between what amounts does the balance in the trust account fluctuate if it earns 6% compounded monthly?

Question 76

What amount is required to fund a perpetuity that pays $10,000 at the beginning of each quarter? The funds can be invested to earn 5% compounded quarterly.

Question 77

If money can earn 6% compounded annually, what percentage more money is required to fund an ordinary perpetuity paying $1,000 at the end of every year than to fund an ordinary annuity paying $1,000 per year for 25 years?

Question 78

What is the current economic value of an inheritance that will pay $2,000 to the beneficiary at the beginning of every three months for 20 years, starting when the beneficiary reaches 20 years of age, 4½ years from now? Assume that money is worth 6% compounded monthly. (Round to the nearest dollar.)

Question 79

A city sells plots in its cemetery for $1,000 plus an amount calculated to provide for the cost of maintaining the grounds in perpetuity. This cost is figured at $25 per plot due at the end of each quarter. If the city can invest the funds to earn 4.8% compounded annually in perpetuity, what is the price of a plot?

Question 80

A $35,000 loan bearing interest at 10% compounded quarterly was repaid, after a period of deferral, by quarterly payments of $1573.83 over 12 years. What was the time interval between the date of the loan and the first payment?