Deck 11: Annuities: Periodic Payment, Number of Payments, and Interest Rate

Question 1

Heather is planning to invest a constant amount of money at the end of every year for 15 years and then allow her money to accumulate interest for 15 more years without any additional deposits. If her investments earn 11% compounded annually and she must have $650,000 in 30 years, how much will she invest at the end of each of the next 15 years?

A) $3,266
B) $2,167
C) $1,889
D) $3,612
E) $3,949

Answer 1

$3,949

Question 2

Fred must pay a $25,000 obligation one year from now. What end-of-month payments for twelve months would put the creditor in an equivalent financial position if the creditor can earn 9% compounded monthly?

A) $2,186.29
B) $1,863.67
C) $1,998.79
D) $2,170.01
E) $1,983.91

Answer 2

$1,998.79

Question 3

If you have $45,000 earning 9.6% compounded monthly, how much money could you take out of the investment at the end of every year for 10 years?

A) $8,820
B) $7,334
C) $2,819
D) $7,198
E) $2,878

Answer 3

$7,334

Question 4

What annual deposit should Martina make to her RRSP at the end of every year if the funds earn 12% compounded monthly and her goal is to accumulate $1,000,000 at the end of 25 years?

A) $4,000
B) $6,750
C) $7,500
D) $12,750
E) $13,358

Question 5

Vince has $35,000 to purchase an annuity that will provide him with equal payments at the end of every three months for the next six years. If the funds earn 8% compounded quarterly, what is the size of the quarterly payments he will receive?

A) $2,335
B) $1,850
C) $3,734
D) $3,324
E) $7,571

Question 6

How much will Clarence have to invest at the end of every year at 11% compounded annually if he is going to accumulate $25,000 in five years?

A) $2,758.93
B) $3,870.52
C) $4,014.25
D) $4,989.01
E) $5,562.50

Question 7

The interest rate charged on a loan of $85,000 is 7.75% compounded annually. If the loan is to be paid off over seven years, calculate the size of the annual payments.

A) $13,084
B) $1,314
C) $9,599
D) $16,187
E) $17,492

Question 8

An investment of $25,000 is made for a 10-year term. After the term expires, equal withdrawals will be made at the end of every month for 15 years. What will the size of the monthly withdrawal be if the investment earns 9% compounded monthly for both the deposit and withdrawal periods.

A) $253.57
B) $161.95
C) $621.58
D) $251.68
E) $616.96

Question 9

What regular investment, made at the end of every three months and earning 10% compounded quarterly, would accumulate to $475,000 in 20 years?

A) $3,492.86
B) $17,616.21
C) $7,856.83
D) $1,912.37
E) $7,916.67

Question 10

A 25-year annuity is purchased for $650,000. Determine the payments it will deliver on a quarterly basis if the rate of interest is 5.05% compounded monthly.

A) $10,554.66
B) $11,004.66
C) $11,504.66
D) $12,004.66
E) $12,554.66

Question 11

Marvin hopes to accumulate $1,000,000 in his retirement plan by making equal contributions at the end of each month for 35 years. He is planning to earn 10.8% compounded monthly. What amount should he deposit every month?

A) $119.90
B) $213.87
C) $569.05
D) $963.27
E) $2,380.95

Question 12

Calculate the size of the monthly mortgage loan payment if a $121,500 loan at 7% compounded semi-annually is to be paid off over 18 years.

A) $983.75
B) $990.84
C) $998.00
D) $598.80
E) $716.44

Question 13

A loan of $17,200 at 9% compounded monthly is to be paid off by equal payments to be made at the end of every month for three years. What is the size of the monthly payment?

A) $561.48
B) $679.49
C) $606.78
D) $477.78
E) $546.96

Question 14

If a single sum of $25,000 is invested at age 25 at 13% compounded annually, what amount will the investor be able to withdraw from the savings, at the end of every month for 20 years, beginning at age 65? At age 65 the investor will put his money into a safer investment that earns only 6% compounded monthly.

A) $13,831
B) $18,567
C) $23,782
D) $41,009
E) $7,185

Question 15

Vanessa wants to retire in 25 years with enough saved to be able to withdraw $5,000 monthly for 20 years. She has already accumulated $48,000 in her investment account. Assume that the rate of interest is 4.8% compounded annually for the 25 years of her contributions, and changes to 3.6% compounded monthly for the next 20 years. Determine what annual contributions she has to make for the next 25 years in order to meet her objective.

A) $38,449.13
B) $22,923.85
C) $20,202.68
D) $18,468.85
E) $15,066.33

Question 16

Today, Barry reached his 50^th birthday and he has $70,000 in his retirement fund. His goal is to have $500,000 on his 65^th birthday. He can expect his investments to earn 13% compounded semi-annually. How much will he have to invest at the end of every six months for the next 15 years in order to reach his goal?

A) $4,978.30
B) $1,722.84
C) $428.30
D) $926.14
E) $2,388.89

Question 17

A loan of $45,000 calls for equal payments at the end of every three months for the next six years. What is the size of the payments if the interest rate is 14% compounded semi-annually?

A) $3,924
B) $2,802
C) $3.817
D) $2,785
E) $3,395

Question 18

If the invested funds earn 13% compounded quarterly what amount invested at the end of every six months for 15 years will accumulate to $295,000?

A) $23,415
B) $22,838
C) $5,953
D) $1,649
E) $3,352

Question 19

Given the time-value of money of 11% compounded annually, calculate the size of the month-end payments for the next five years that would be equivalent to a single payment of $13,285 payable five years from now.

A) $285.42
B) $221.42
C) $169.39
D) $177.76
E) $299.54

Question 20

Sally has invested a constant amount at the end of every six months for the last 40 years. She has made wise investment decisions and has earned a return of 16.4% compounded semi-annually. Today the value of her savings has reached $2,500,000. What amount has she been investing every half-year?

A) $91.66
B) $375.29
C) $5,834.15
D) $61,983.84
E) $205,375.29

Question 21

Vince has $35,000 to purchase an annuity that will provide him with payments of $1,000 at the end of every three months. If the funds earn 8% compounded quarterly, how long will the payments continue?

A) 35 years
B) 36 years
C) 15 years
D) 9 years
E) 60 years

Question 22

Martina's RRSP earns 12% compounded monthly and her goal is to accumulate $1,000,000 by making deposits of $4,100 at the end of every year. How many years will it take to reach her goal?

A) 24 years
B) 29 years
C) 33 years
D) 47 years
E) 125 years

Question 23

A loan of $25,000 is to be repaid by monthly payments of $400. The interest rate is 9% compounded monthly. How many months will it take for the amount owing on the debt to be reduced to less than $10,000?

A) 57
B) 68
C) 74
D) 85
E) 92

Question 24

A $350,000 loan has an interest rate of 6.2% compounded semi-annually. Determine the semi-annual payments that will reduce the balance to $80,000 after 4 years

A) $47,909.55
B) $45,089.24
C) $44,224.58
D) $42,806.17
E) $41,105.65

Question 25

How many monthly withdrawals of $1,400 will an investment of $75,000 sustain if the first withdrawal is made 13 months from now and the money earns 8.4% compounded monthly?

A) 96
B) 75
C) 66
D) 53
E) 45

Question 26

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, Moses will, at the end of every six months, take $20,000 out of his Retirement Fund. For how long will he be able to do that before the money runs out?

A) 15.4 years
B) 35.0 years
C) 20.0 years
D) 12.9 years
E) 17.5 years

Question 27

A loan of $16,525 at 10.8% compounded monthly is to be paid off by equal monthly payments of $650. How long will it take to pay off the loan?

A) 26 months
B) 29 months
C) 32 months
D) 36 months
E) 48 months

Question 28

MaryAnne is taking out a loan of $70,000 at 8% compounded semi-annually. Calculate the monthly payments that will reduce her balance owing to $30,000 in five years.

A) $2,968
B) $1,005
C) $809
D) $669
E) $666

Question 29

Five years before her daughter was expected to enter college, Frieda deposited $15,000 in an education fund. Her daughter will make 48 equal quarterly withdrawals from the fund starting on the date she enters college. If the education fund earns 10% compounded quarterly, what will be the maximum quarterly withdrawal?

A) $863.41
B) $540.09
C) $526.92
D) $263.92
E) $885.00

Question 30

How many monthly payments of $919 will it take to pay off a mortgage loan if a $121,500 loan at 7% compounded semi-annually?

A) 132
B) 178
C) 212
D) 236
E) 249

Question 31

Marvin's goal is to accumulate $1,000,000 in his retirement plan by making contributions of $250 at the end of each month. He expects to earn 10.8% compounded monthly. How long will it take Marv to reach his goal? (rounded up to the nearest whole year)

A) 34 years
B) 41 years
C) 155 years
D) 14 years
E) 26 years

Question 32

Jenny has two investments. The first is a trust fund that was setup 18 years ago when she was born with a lump sum deposit of $25,000 earning 4.8% interest compounded annually. The second investment is a fund setup two years ago that Jenny contributes $800 per quarter. This fund earns 3.1% compounded semi-annually. Determine Jenny's total investment value 20 years from now.

A) $266,665.73
B) $296,665.73
C) $302,665.73
D) $366,665.73
E) $396,665.76

Question 33

If deposits of $9,900 invested at the end of every six months earn 13% compounded quarterly, how long will it take to accumulate $295,000?

A) 4.25 years
B) 8.5 years
C) 17.0 years
D) 34.0 years
E) 68.0 years

Question 34

A loan of $47,000 calls for payments of $2,700 at the end of every three months until the debt is settled. At an interest rate of 14% compounded semi-annually, how many payments will be made?

A) 14
B) 17
C) 24
D) 27
E) 40

Question 35

Clarence has been investing $1,000 at the end of every year at 11% compounded annually. With today's contribution his investment has grown to $44,500. How many years ago did he make the first contribution?

A) 26 years
B) 49 years
C) 17 years
D) 31 years
E) 12 years

Question 36

Given the time-value of money of 11% compounded annually, calculate the term of an ordinary annuity of $425 monthly payments with a future value of $37,725.

A) 66.0 years
B) 33.0 years
C) 14.3 years
D) 11.0 years
E) 5.5 years

Question 37

For a long time, Sally has been investing $7,000 at the end of every six months. The value of her savings today is $2,500,000. She has made wise investment decisions and has earned a return of 16.4% compounded semi-annually. How long ago (rounded off to the nearest whole year) did Sally start this savings plan?

A) 17 years
B) 22 years
C) 27 years
D) 32 years
E) 41 years

Question 38

Bosley has $750,000 which is earning 7.2% compounded monthly. At the end of every month for the next 10 years he plans to withdraw $5,000. After that he wants to increase his equal monthly withdrawals to the largest amount possible for 15 more years. What is that amount?

A) $5,733
B) $5,917
C) $6,029
D) $6,315
E) $6,977

Question 39

You have $45,000 earning 9.6% compounded monthly. For how long will you be able to withdraw $5,000 at the end of every year?

A) 10.7 years
B) 13.9 years
C) 21.8 years
D) 24.4 years
E) 29.5 years

Question 40

If $2,000 were invested at the end of every three months, how long would it take to accumulate $475,000 at 10% compounded quarterly? (rounded up to the nearest whole year)

A) 60 years
B) 79 years
C) 27 years
D) 20 years
E) 14 years

Question 41

A stereo priced at $1,057.53 was paid for by 12 monthly payments of $100 with the first payment made one month after the date of purchase. What monthly compounded nominal interest rate was charged?

A) 2.00%
B) 2.33%
C) 27.97%
D) 24.00%
E) 24.96%

Question 42

When Barry reaches his 40^th birthday he will receive $10,000 which he will put into his retirement fund. His goal is to have $500,000 in the retirement fund on his 65^th birthday. To reach his goal, he will make equal deposits of $1,520 at the end of every six months leading up to his 65^th birthday. He can expect his investments to earn 13% compounded semi-annually. At what age must he start the semi-annual deposits of $1,520 in order to reach his goal?

A) 25
B) 30
C) 35
D) 40
E) 45

Question 43

How much longer will it take for an initial deposit of $10,000 and annual payments of $1,000 accumulate to $25,000 if interest was at 4.11% compounded annually versus 5.45% compounded annually.

A) 1 year
B) 2 years
C) 3 years
D) 4 years
E) 5 years

Question 44

A $10,000 debt is repaid by payments of $800 at the end of each quarter for five years. What quarterly-annually compounded nominal interest rate was charged on the loan?

A) 23.10%
B) 4.96%
C) 11.08%
D) 9.81%
E) 19.86%

Question 45

A life insurance company will sell a 20-year annuity paying $1,600 at the end of each month for $175,000. What annual compounded nominal rate of interest will the annuitant earn?

A) 9.401%
B) 8.735%
C) 9.226%
D) 9.335%
E) 9.297%

Question 46

A $50,000 mortgage loan requires monthly payments of $520 for 20 years. What is the annually compounded nominal rate of interest on the loan?

A) 11.3752%
B) 11.6987%
C) 11.1146%
D) 0.9381%
E) 11.2573%

Question 47

Corey has $50,000 deposited in an account earning 6.2% compounded monthly. He plans to withdraw $2,000 per month for two years. Afterwards, he plans to replenish his account by contributing $3,000 per quarter to bring his investment back to the original $50,000. Determine how many payments will be needed for the quarterly payments.

A) 15
B) 14
C) 13
D) 17
E) 11

Question 48

What monthly compounded nominal rate of return must Rachel earn in her RRSP in order for month-end contributions of $600 to accumulate to $750,000 in 25 years?

A) 8.04%
B) 9.65%
C) 10.09%
D) 11.48%
E) 13.50%

Question 49

What compounded rate of return will allow investments of $800 at the end of every six months to accumulate to $24,000 after 10 years?

A) 14.876%
B) 8.062%
C) 8.143%
D) 8.309%
E) 15.286%

Question 50

Janice has $200,000 in an investment and wishes to use this money to take time off and get her Master's degree. She plans to withdraw $2,000 per month for the first 3 years for her monthly expenses. Afterwards, she intends to increase her withdrawals to $3,000 per month. Determine how many monthly payments can be extracted after the third year if interest throughout is 5.2% compounded monthly.

A) 59 months
B) 60 months
C) 61 months
D) 62 months
E) 63 months

Question 51

A $15,000 deposit earns 6% compounded quarterly. Rounded to the nearest month, how long (before the first withdrawal) must the deposit be allowed to grow before it can provide 24 quarterly withdrawals of $1,200.

A) 7 years
B) 7 years and 3 months
C) 7 years and 11 months
D) 8 years and 3 months
E) 8 years and 5 months

Question 52

Mr. Johnston has been investing $5,000 into his savings plan at the end of every year for the last 17 years. His investments have earned 10.6% compounded semi-annually. If he increases his annual contributions to $6,000, how much longer will it take for his savings plan to reach $1,000,000?

A) 9 years
B) 11 years
C) 13 years
D) 15 years
E) 17 years

Question 53

What would be the effective rate of interest if $100,000 was accumulated by investments of $3,500 made at the end of every three months for five years?

A) 15.20%
B) 14.40%
C) 8.65%
D) 13.12%
E) 34.61%

Question 54

It was estimated that a famous baseball player with a personal fortune of $40 million dollars depleted his funds by spending $1,500,000 and over a period of time became $60 million in debt. If interest is at 3.8% compounded monthly, determine how long it took for the player to get into this situation.

A) 75 months
B) 70 months
C) 76 months
D) 82 months
E) 88 months

Question 55

Clarence has a retirement fund of $300,000 that earns 11% compounded monthly. His plan is to withdraw $3,000 at the end of every month for 12 years and then increase the monthly withdrawals to $5,000. How many $5,000 withdrawals will he be able to make?

A) 30
B) 43
C) 48
D) 51
E) 59

Question 56

Determine how much faster monthly payments of $248.69 will accumulate to $10,000 if interest is at 7.2% compounded monthly, compared to monthly payments of $182.61 at 6.6% interest compounded monthly.

A) 6 months
B) 8 months
C) 10 months
D) 12 months
E) 14 months

Question 57

Determine how long a $45,000 deposit will sustain quarterly withdrawals of $800 if interest is at 6.14% compounded annually.

A) 100 quarters
B) 125 quarters
C) 150 quarters
D) 175 quarters
E) 200 quarters

Question 58

For the next 15 years Andre expects to earn 12% compounded semi-annually on the Retirement Savings Plan (RSP) that he is starting. For the subsequent 10 years he expects a return of 7% compounded semi-annually. How much money is he planning to have in 25 years if he invests $3,500 at the end of every six months for the 25 years?

A) $411,922
B) $610,059
C) $382,600
D) $451,603
E) $1,068,912

Question 59

Heather's investments will earn 11% compounded annually and, in 30 years, she must have $645,000. For the next 20 years she can make year-end contributions of $10,000. She will not be able to make any contributions after 20 years from now. She wants to know if she has to start the $10,000 annual contributions now in order to reach her goal. If not, how many years can she wait before starting the $10,000 annual contributions?

A) She must start now.
B) She can wait for 4 years.
C) She can wait for 8 years.
D) She can wait for 12 years.
E) She can wait for 16 years.

Question 60

A $12,000 loan is repaid by semi-annual payments of $1,500 each. Interest on the loan is 10% compounded semi-annually. How long will it take to pay off the loan?

A) 5.5 years
B) 5 years
C) 21 years
D) 10 years
E) 10.5 years

Question 61

A loan of $88,700 can be paid off by monthly payments of $1,000 for 11 years. What is the annually compounded nominal interest rate?

A) 9.81%
B) 6.45%
C) 7.74%
D) 7.86%
E) 8.02%

Question 62

What annually compounded rate of return must Rachel earn in her RRSP in order for month-end contributions of $450 to accumulate to $750,000 in 25 years?

A) 12.26%
B) 9.43%
C) 10.71%
D) 11.32%
E) 11.93%

Question 63

Inflation is a major concern for economists. Many are predicting higher inflation rate in the coming year. If a loaf of bread cost $1.99 last year and is now $2.25, determine the annual rate of inflation.

A) 13.06%
B) 11.08%
C) 10.28%
D) 9.54%
E) 8.63%

Question 64

You have the option receiving $4,000 at the end of every six months for 15 years or a single lump sum of $250,000 at the end of the 15 years. What effective interest rate would make the two options equal in value?

A) 9.500%
B) 4.642%
C) 9.770%
D) 5.250%
E) 9.285%

Question 65

Royal Niagara Golf and Country Club allows members to pay the annual membership fee by a single payment of $11,000 at the beginning of the year or by payments of $1,000 at the end of each month. What monthly compounded nominal rate of interest is being paid by members who select the monthly plan?

A) 19.166%
B) 16.376%
C) 15.972%
D) 17.663%
E) 21.845%

Question 66

A $10,000 deposit along with quarterly contributions of $150 accumulates to $18,000 in 5 years. Determine the nominal rate of interest if interest is compounded annually.

A) 7.58%
B) 8.58%
C) 9.68%
D) 10.28%
E) 13.28%

Question 67

A lottery winner must decide between receiving $5,000 at the end of every month for 10 years or one lump sum of $1,000,000 after 10 years. What annually compounded nominal rate of interest would make the two options equal in value?

A) 10.152%
B) 7.984%
C) 9.774%
D) 7.807%
E) 9.580%

Question 68

David and Hana plan to purchase a house in 5 years' time. David already has $20,000 that he invested in an account two years ago that is earning 0.308% interest compounded monthly. Hanna plans to contribute $675 per month for the next 5 years into her account. Determine what the nominal rate of interest (based on monthly compounding) that Hanna's investment should earn if their combined savings is to total $70,000.

A) 3.07%
B) 4.22%
C) 3.68%
D) 4.04%
E) 4.59%

Question 69

A loan of $25,000,000 is to be repaid by annual year-end payments of $3,000,000 for 30 years. What is the effective interest rate on this loan?

A) 9.746%
B) 43.62%
C) 3.600%
D) 11.548%
E) 21.598%

Question 70

One payment stream is being compared to another. The first option is for $500 semi-annual payments over 5 years at an interest rate of 6% compounded semi-annually. The second option is for $250 quarterly payments over 5 years, with interest compounded quarterly. Determine the nominal rate of interest to be offered on the second option for both options to have equal future values.

A) 4.95%
B) 5.25%
C) 5.65%
D) 6.05%
E) 6.85%

Question 71

A life insurance company advertises that $75,000 will purchase a 25-year annuity paying $456.10 at the end of each month. What monthly compounded nominal rate of return does the annuity investment earn?

A) 5.4%
B) 6.2%
C) 5.7%
D) 5.6%
E) 4.5%

Question 72

A life insurance company advertises that $50,000 will purchase a 20-year annuity paying $402.80 at the end of each month. What effective rate of return does the annuity investment earn?

A) 6.15%
B) 6.92%
C) 7.76%
D) 7.18%
E) 7.50%

Question 73

What effective interest rate will Frankie have to earn if his investments of $2,000 at the end of every three months for 20 years are to have a maturity value in 20 years of $1,000,000?

A) 11.56%
B) 13.81%
C) 15.29%
D) 16.19%
E) 17.49%

Question 74

David has the option to pay for auto insurance on either a lump sum basis of $2,000 per year or $180 per month. Determine the effective rate of interest (based on monthly compounding) if David chooses the monthly payment option.

A) 11.52%
B) 12.45%
C) 13.52%
D) 14.52%
E) 15.45%

Question 75

Susan's car loan payments are $265.08 at the end of each month for four years. The amount she borrowed was $12,000. What is the monthly compounded nominal interest rate?

A) 6.500%
B) 2.900%
C) 10.500%
D) 4.750%
E) 6.000%

Question 76

After 12 ½ years contributions of $750 at the end of each semi-annual period has accumulated into $24,510.47. If interest rate is compounded semi-annually, determine the effective annual rate of the investment.

A) 8.08%
B) 8.62%
C) 9.08%
D) 9.58%
E) 10.08%

Question 77

After 15 years of contributions of $3,500 at the end of every six months to a Retirement Savings Plan, the accumulated amount stood at $232,536. What semi-annually compounded nominal rate of return was earned by the funds in the RSP?

A) 2.5%
B) 5.0%
C) 7.5%
D) 10.0%
E) 12.5%

Question 78

What monthly compounded nominal rate of return would one need to achieve in order to have investments of $100 made at the end of every month for 35 years to accumulate to $1 million?

A) 14.50%
B) 14.76%
C) 13.62%
D) 12.93%
E) 11.35%

Question 79

The Jacksons have agreed to pay $1,419 at the end of every month for 15 years on their mortgage loan of $167,000. What annually compounded nominal rate are they paying?

A) 5.09%
B) 7.23%
C) 8.11%
D) 7.29%
E) 6.11%

Question 80

Malcolm wants to purchase an annuity that will pay him $7,000 at the end of every three months for 15 years. His financial advisor has told Malcolm that this annuity will cost him $250,000. What annually compounded nominal interest rate was used in this calculation?

A) 7.56%
B) 9.3%
C) 12.60%
D) 18.89%
E) 22.67%