Deck 3: Simple Annuities

Question 1

Drew Wallace has made deposits at the end of each year into a registered savings account for the past 10 years,with his final deposit being made today.He deposited $2500 for the first 5 years and $2000 for the last 5 years.The account earned interest at j = 8%.How much is in his account today (just after his final deposit)? (answer to the nearest dollar)

A)$17,967
B)$22,652
C)$26,400
D)$33,283

Answer 1

$33,283

Question 2

A payment of $25,000 is due on January 1,2014.To accumulate enough money to make this required payment,monthly deposits of $R were made into an account earning j12 = 6% starting on June 1,2012.If the last deposit is made on January 1,2014,what is R?

A)$1257.56
B)$1191.66
C)$1251.30
D)$1185.73

Answer 2

$1191.66

Question 3

You deposit $300 every 3-months.Your first deposit is made November 8,2009 and your final deposit is made November 8,2017.If the deposits earn j₄ = 8%,how much do you have immediately after the deposit on November 8,2017?

A)$13,833.47
B)$13,533.47
C)$13,268.11
D)$12,713.83

Answer 3

$13,833.47

Question 4

Deposits of $2000 are made every 6-months for 6-years in a fund that pays interest at j₂ = 8%.Just after the 12^th deposit,the interest rate changes to j₄ = 8% and quarterly deposits of $1000 are now made,first deposit 3 months after the interest rate change.How much is in the fund immediately after the 20^th deposit of $1000?

A)$54,348.98
B)$68,495.94
C)$68,781.09
D)$68,952.48

Question 5

You deposit $3000 every 6-months into a fund earning interest at j₂ = 7%.Immediately after the 9^th deposit,the interest rate changes to j₂ = 6%.How much is in your fund immediately after the 20^th deposit?

A)$69,528.87
B)$81,292.71
C)$81,480.66
D)$83,836.46

Question 6

You make quarterly deposits of $500.The first 12 deposits earn j₄ = 6%.Immediately after the 12^th deposit,the interest rate changes to j₄ = 4%.How much have you accumulated immediately after the 20^th deposit?

A)$11,561.83
B)$11,488.25
C)$11,203.72
D)$10,663.44

Question 7

Deposits of $1500 are made every 3 months starting today,October 5,2010.The final deposit is made on January 5,2015.If the fund earns j₄ = 8%,how much is in the fund immediately after the deposit on January 5,2015?

A)$30,018.11
B)$30,618.47
C)$32,118.47
D)$34,260.84

Question 8

You begin making monthly deposits of $400 on June 3,2007 in a fund earning j₁₂ = 9%.How much do you have in the fund immediately after the deposit on October 3,2010?

A)$19,661.32
B)$19,117.93
C)$18,578.59
D)$14,073.23

Question 9

Billy deposits $500 every 3-months in a fund earning interest at j₄ = 8%.After 24 deposits,the interest rate changes to j₄ = 6%.What is the accumulated value at the time of the 40^th deposit?

A)$29,847.53
B)$28,692.67
C)$28,268.64
D)$24,177.12

Question 10

Ken Tuckey takes out a loan today to be repaid with quarterly payments of $688.64 over 4 years (first payment 3 months from today).If the interest rate on the loan is j₄ = 7.2%,how much total interest does Ken pay over the life of the loan?

A)$3138.28
B)$1620.04
C)$1518.24
D)$1018.24

Question 11

A loan is to be repaid with semi-annual payments of $2000 over 8 years,first payment due in 6 months.The interest rate on the loan is j₂ = 10% for the first 3 years and j₂ = 6% thereafter.What is the amount of the loan? (answer to nearest dollar)

A)$21,676
B)$22,882
C)$24,439
D)$27,212

Question 12

Deposits of $200 are made at the end of every 3-months.The interest rate is j4 = 6% for the first 4-years (16 deposits)and j4 = 5% thereafter.What is the accumulated value of the deposits,immediately after the 24th deposit?

A)$5632.99
B)$5711.91
C)$5258.25
D)$5703.40

Question 13

An investor wants to accumulate $10,000 at the end of 15 years by making 11 annual deposits of $R,1^st deposit to be made at the end of year 4.If j₁ = 7%,what is R?

A)$559.01
B)$592.12
C)$614.93
D)$663.57

Question 14

The accumulated value of n payments of $500 at i immediately after the n^th payment is S.Which of the following gives the correct accumulated value immediately after the (n+2)^th payment of $500?

A)S(1 + i)+ 2(500)(1 + i)
B)S + 500(1 + i)+ 500
C)[S + 500](1 + i)² + 500
D)S(1 + i)² + 500(1 + i)+ 500

Question 15

A loan,A,is repaid with semi-annual payments of $1000.The first payment is due May 26,2007 and the last payment is due May 26,2012.If the interest rate on the loan is j₂ = 7% and the loan was taken out on November 26,2006,what is A?

A)$8316.61
B)$8607.69
C)$9001.55
D)$9316.61

Question 16

Billy deposits $800 at the end of every 3-months in a fund earning interest at j4 = 12%.At the end of 3 years,the interest rate changes to j4 = 8%.What is the accumulated value immediately after his 20th deposit?

A)$18,220.00
B)$20,168.95
C)$21,248.81
D)$21,496.30

Question 17

Monthly deposits of $800 are made into a fund starting today,April 14,2006 and continuing until July 14,2008.The fund earns j₁₂ = 6%.What is the accumulated value of these deposits on July 14,2008?

A)$23,099.52
B)$23,179.62
C)$23,979.62
D)$24,064.30

Question 18

Mrs.Gerri Atric decides to save money for her retirement.She makes monthly deposits of $150 starting on November 7,2012 and continuing to April 7,2015.If her deposits are earning j₁₂ = 8%,how much money will she have on April 7,2015?

A)$4781,45
B)$4813.33
C)$4963.33
D)$5146.42

Question 19

You are given S = accumulated value of n payments of $1 at the time of the n^th payment.Which of the following will give the correct result for the accumulated value of n+ 1 payments of $1,one period after the (n+ 1)^th payment?

A)[S (1 + i )+ 1](1 + i
B)[S + 1](1 + i )
C)S (1 + i )² + 1
D)S (1 + i)+ 1

Question 20

Deposits of $R are made every 3 months starting June 15,2010 in a fund paying interest at j₄ = 8%.Immediately after the deposit on December 15,2018,there is $40,000 in the fund.What is R?

A)$800.09
B)$832.75
C)$867.46
D)$943.85

Question 21

Charles invests $500 on his birthday from age 18 to age 29 (inclusive).If his deposits earn j₁ = 9%,how much will he have on his 65^th birthday? (answer to nearest dollar)

A)$205,576
B)$224,078
C)$244,245
D)$266,227

Question 22

Cam has just won $1 million in the lottery.He plans to spend half of it now and invest the rest in an annuity that has semi-annual payments for the next 30 years,first payment 6 months from now.If money is worth j₂ = 8%,what is the size of the semi-annual payment?

A)$44,413.72
B)$44,201.85
C)$22,984.96
D)$22,100.92

Question 23

Gary has determined he wants an annuity paying $10,000 a year for 10 years,with the first payment payable on his 60^th birthday.If j₁ = 8%,what single deposit must he make on his 40^th birthday to fund this annuity?

A)$13,329.96
B)$14,396.36
C)$15,548.07
D)$16,791.91

Question 24

A loan of $A is to be repaid over 5 years with quarterly payments of $600 (1^st payment 3 months from now).The interest rate on the loan is j₄ = 8% for the first 3 years and j₄ = 6% thereafter.What is the value of A?

A)$10,836.76
B)$10,220.67
C)$10,101.89
D)$9,886.77

Question 25

If the accumulated value of n-payments of $250,at the time of the n^th payment,is $13,606.35,what is the accumulated value of (n-1)payments of $300,one interest period after the last payment?

A)$16,027.62
B)$16,327.62
C)$16,627.62
D)Cannot be determined without knowing the interest rate

Question 26

What is the present value of monthly payments of $1000 for 5 years followed by monthly payments of $500 for 10 years (first payment one month from now)if j₁₂ = 4.8%?

A)$89,485.08
B)$90,692.96
C)$100,826.85
D)$115,238.16

Question 27

Jacques takes out a loan and agrees to pay it back with payments of $500 at the end of every 6-months for 10 years at j2 = 8% (20 payments in total).He makes the first 3 payments (time 1 to 3),but misses the next 3 (time 4 to 6).What single payment would he need to pay at the time of the 7th payment (time 7)that would make up for the 3 missed payments AND pay off the remaining payments?

A)$4992.82
B)$5492.82
C)$6326.15
D)$7116.05

Question 28

Betty,who just turned 17 today,receives an inheritance of $A.She will receive $5000 every 6 months for 10 years,starting the day she turns 25.If j₂ = 8%,what is A?

A)$67,951.50
B)$37,731.06
C)$36,712.08
D)$36,279.86

Question 29

Jim just turned age 65.He takes his RRSP savings of $300,000 and buys a 20-year annuity that pays him $R every month.If the interest rate is j₁₂ = 7.2% and the first payment is at age 65,what is R?

A)$2376.22
B)$2366.48
C)$2362.05
D)$2347.96

Question 30

A man has won a lottery worth $500,000.He invests this money in a fund paying j₂ = 7%.He plans to withdraw $R every 6 months for 25 years,with the first withdrawal made today.What is R?

A)$21,445.20
B)$21,316.85
C)$20,596.00
D)$20,452.63

Question 31

A loan of $10,000 is taken out today and is to be repaid over 2-years with weekly payments of $R at j₅₂ = 10.4%,first payment one week from today.What is R?

A)$86.60
B)$101.34
C)$106.60
D)$111.40

Question 32

An individual borrows $10,000 at j₄ = 8%.He/she is to pay off this loan with quarterly payments of $R over 10-years (first payment 3-month after loan is taken out).What is R?

A)$338.75
B)$358.39
C)$365.56
D)$431.78

Question 33

Bank A offers you a loan which you will repay over 5-years at j₁₂ = 6% with monthly payments of $1500.Bank B offers you the same loan amount,but at j₄ = 6%,which you will repay over 5-years with quarterly payments of $R.What is the maximum value of R for you to even consider Bank B?

A)$4525.88
B)$4522.54
C)$4519.19
D)$4500.00

Question 34

The present value at j₁₂ of a $10,000 payment today,followed by 32 monthly payments of $5000 is $136,335.69.What is the present value of 33 monthly payments of $2000,first payment made today,if these payments earn the same interest rate,j₁₂?

A)$48,534.28
B)$50,534.28
C)$52,534.28
D)Cannot be determined without knowing the value of j₁₂

Question 35

You wish to have $25,000 on September 1,2012 to buy a new car.What monthly deposit is needed to achieve your goal if you can earn j₁₂ = 5.4% and you make monthly deposits from October 1,2007 to September 1,2012?

A)$363.88
B)$370.91
C)$476.38
D)$483.41

Question 36

A deposit of $10,000 is made today.Semi-annual withdrawals of $R are made for 15-years,first withdrawal made 6-months from today.The fund earns interest at j₂ = 10% for the first 6-years and j₂ = 6% thereafter.What is R?

A)$618.93
B)$605.26
C)$540.26
D)$442.15

Question 37

You borrow $A on September 28,2009 at j₁₂ = 6%.You repay the loan with monthly payments of $250 starting October 28,2009 and ending on October 28,2012.What is the value of A?

A)$10,133.20
B)$9834.03
C)$8425.63
D)$8217.75

Question 38

An individual buys $15,000 worth of furniture.They make a down payment of $5000 and pay off the rest of their bill with quarterly payments of $R for 10 years.If j₄ = 8% and the first quarterly payment is made 3 months after the loan is advanced,what is R?

A)$543.34
B)$365.56
C)$358.39
D)$338.75

Question 39

Gerry wins a lottery worth $100,000.Instead of the lump sum,Gerry will be paid in monthly installments for a total of 60 payments,with the first monthly payment to be made today.If the money earns interest at j₁₂ = 6%,what is the monthly payment?

A)$1933.28
B)$1923.66
C)$1433.28
D)$1426.15

Question 40

You own shares in the XYZ company.For the first 10 years that you owned the shares,they paid a dividend of $150 every 6 months (paid at the end of every 6 months).However due to a downturn in the economy,no dividend has been paid in the past 2 years.If you have reinvested the dividends in a fund earning j₂ = 5%,how much do you have today?

A)$4229.48
B)$4224.45
C)$4126.32
D)$3831.70

Question 41

Sally deposits $10,200 today in a fund earning interest at j₂ = 6%.She wishes to withdraw $600 every 6 months for as long as possible,with the first withdrawal made today.Including the withdrawal made today,how many full withdrawals of $600 would she be able to make?

A)22
B)23
C)24
D)25

Question 42

Trish needs to have $20,000 one year from now.She plans to make 9 equal monthly deposits,first deposit made today.What is the size of each deposit needed if the money is deposited into an account paying j₁₂ = 6%?

A)$2135.12
B)$2145.80
C)$2156.53
D)$2178.15

Question 43

To buy a used car,you have two options.You can pay $10,400 in cash today (December 12,2014)or you can pay $R every month,from December 12,2014 and to July 12,2017.If the interest rate is j₁₂ = 6%,what is R?

A)$352.50
B)$362.99
C)$350.75
D)$361.19

Question 44

You can buy a used car for cash of $A on August 12,2010,OR make quarterly payments of $500,starting August 12,2010 and finishing on August 12,2016.If the loan charges interest at j₄ = 4%,what is the value of A?

A)$10,621.69
B)$10,727.91
C)$11,011.58
D)$11,121.69

Question 45

A $1000 loan is being paid off with annual payments of $100 at the end of each year for as long as necessary,with the final $100 payment increased by a balloon payment.If j₁ = 3.5%,what is the size of the balloon payment?

A)$30.27
B)$33.67
C)$50.87
D)$52.66

Question 46

You deposit $100 every three months for the next 50 years,first deposit made today.If the interest rate is j₄ = 10%,how much do you have three months after your last deposit?

A)$582,417
B)$568,212
C)$568,112
D)$554,256

Question 47

Deposits of $725 are made into an account earning j₄ = 10% in order to accumulate to $21,500.It turns out that 22 deposits are needed,plus a bit more.If the final deposit is a drop payment made 3 months after the last regular deposit,what is the size of this final deposit?

A)$588.79
B)$574.43
C)$51.29
D)$0

Question 48

A university student wins a scholarship worth $50,000.Instead of the lump sum,she chooses to be paid by 48 monthly payments of $R,with the first monthly payment to be made 5 months from now.If the money earns interest at j₁₂ = 9%,what is the monthly payment?

A)$1291.62
B)$1282.00
C)$1272.46
D)$1244.25

Question 49

Jim buys some furniture for $3850.He pays $200 down and repays the rest with 24 monthly payments of $R,first payment due 3 months from today.If j₁₂ = 9%,what is R?

A)$169.26
B)$170.53
C)$178.53
D)$179.87

Question 50

An education fund of $40,000 is to be accumulated by making payments of $400 at the end of every 3-month period,plus a smaller concluding payment.Determine the number of full payments required if j₄ = 9%.

A)50
B)51
C)52
D)53

Question 51

Mrs.Smith makes 20 annual deposits of $2000 into a retirement savings account,first deposit made today.If she earns j₁ = 5% on her money,how much does she have 25 years from today?

A)$66,131.91
B)$84,402.94
C)$88,623.08
D)$95,454.20

Question 52

Mr.A deposits $5000 today in a fund earning interest at j₂ = 6%.He wishes to withdraw $490 every 6 months for as long as possible.He will make his first withdrawal exactly 2 years from today.When will he make the final smaller concluding (drop)withdrawal?

A)End of 6.5 years
B)End of 7 years
C)End of 8.5 years
D)End of 9 years

Question 53

You buy furniture today for $A and "don't pay a cent for 6 months".At the end of 6 months,you begin making monthly payments of $125 for 36 months.If this payment plan charges interest at j₁₂ = 7.2%,what is A?

A)$3870.81
B)$3894.04
C)$3917.40
D)$4036.34

Question 54

Sally wants to accumulate $11,500.She makes deposits of $500 at the end of every 6 months in a fund earning interest at j₂ = 5%.It turns out that after making 18 deposits,she is still short of her goal by $306.83.What is the size of the smaller concluding deposit (drop payment)needed 6 months later in order for her to reach (or exceed)her goal of $11,500?

A)$27.00
B)$185.50
C)$314.50
D)No deposit is needed 6 months later

Question 55

A loan of $10,000 is to be repaid by 60 monthly payments of $205.00 plus a smaller concluding payment made one month after the last $205 payment.Payments begin one month from now.If j₁₂ = 9%,find the amount of the smaller final payment.

A)$124.46
B)$135.62
C)$194.86
D)$196.32

Question 56

To buy some furniture,you can put $150 down and "don't pay a cent" for 6 months.At the end of 6 months,you begin making monthly payments of $100 for 2-years.If j₁₂ = 8.4%,what is the equivalent cash price of the furniture?

A)$2276.68
B)$2261.89
C)$2126.68
D)$2111.89

Question 57

You can buy a car with 60-monthly payments of $350,first payment made today.If j₁₂ = 3%,what is the equivalent cash price of the car,payable today?

A)$19,478.33
B)$19,527.02
C)$19,828.33
D)$20,947.63

Question 58

A company has developed a unique way to allow their employees to accumulate $5000 in order to buy $5000 worth of shares in the company.The company will set up an account for each employee,paying interest at j₁₂ = 12%.At the end of every month the company will deduct an amount from an employee's pay and deposit it into this account (first deduction made 1 month from now).The company has decided to deduct n-payments of $81.25,plus make a smaller concluding deduction one month after the final deduction of $81.25,at which time the employee will have $5000.What is the size of this smaller concluding deduction?

A)$24.08
B)$25.66
C)$25.92
D)No final deduction is needed

Question 59

To buy a car,you are given two options.Option 1 is to pay $20,000 cash today.Option 2 is to make monthly payments of $500 for as long as necessary,first payment made today.If the dealer charges interest at j₁₂ = 5.4%,how many payments are needed,including the very first one,if the final payment is increased by a balloon payment?

A)42
B)43
C)44
D)45

Question 60

Jerry makes semi-annual deposits of $R into a fund paying j₂ = 5%.His first deposit was made on March 15,2011.His last deposit will be made on March 15,2015.On September 15,2015 he has accumulated $15,000 in the fund.What is R?

A)$1470.10
B)$1506.85
C)$1675.13
D)$1717.01

Question 61

A student wishes to accumulate $4000 by making quarterly deposits of $200 into an account,first deposit made on January 1,2011.The account earns interest at j₄ = 6%.What is the size of the final,smaller quarterly deposit (drop payment)and on what date will this final deposit be made?

A)A final deposit of $159.73 is made on July 1,2015
B)A final deposit of $102.12 is made on July 1,2015
C)A final deposit of $159.73 is made on April 1,2015
D)A final deposit of $102.12 is made on April 1,2015

Question 62

You deposit $100 at the end of every month for 7 years.At the end of 7 years you wish to have accumulated $12,600.Using linear interpolation,what nominal rate of interest,j₁₂,is required?

A)11.06%
B)11.15%
C)11.90%
D)11.94%

Question 63

Tae takes out a loan for $5000,to be paid back with monthly payments of $199 for as long as is needed.The first payment of $199 is due exactly 6-months after the loan is taken out.Tae also plans to increase the size of the final payment (that is,he plans to make a balloon payment,not a drop payment).If the interest rate on the loan is j₁₂ = 12%,how many payments are needed?

A)28
B)29
C)30
D)31

Question 64

You buy some furniture for $1200.You have 2 options: pay the $1200 today or make 12 monthly payments (made at the end of every month).For the 2^nd option,the furniture store will charge you an administration fee of $72.Thus,your monthly payment will be 1272 ¸ 12 = $106.Which of the following statements is closest to the truth if you were to choose option 2? (All interest rates are j₁₂)

A)The interest rate you are being charged is 6.00%
B)The interest rate you are being charged is 8.83%
C)The interest rate you are being charged is 10.90%
D)The interest rate you are being charged is 11.66%

Question 65

Sally can buy some furniture for $11,000 cash or monthly payments of $1000 for 1 year,with the first $1000 payment made today.What range contains the interest rate j₁₂ that Sally is being charged?

A)18% < j₁₂ < 19%
B)19% < j₁₂ < 20%
C)20% < j₁₂ < 21%
D)21% < j₁₂ < 22%

Question 66

You plan to make 40-quarterly deposits into a fund in order to have $10,000 at the end of 10 years.Consider the following 3 cases:
a. Deposit $R_I starting today;earn j₄ = x%
b. Deposit $R_II starting 3-months from today;earn j₄ = x%
c. Deposit $R_III starting 3-months from today;earn j₁₂ = x%
Which of the following is true?

A)R_I > R_II ;R_II < R_III
B)R_I > R_II ;R_II > R_III
C)R_I < R_II ;R_II < R_II
D)R_I < R_II ;R_II > R_III

Question 67

A company wishes to accumulate $100,000.To do so,they will make quarterly deposits of $4000 into a fund paying interest at j₄ = 8%.It turns out they need to make 20 deposits,plus a smaller drop payment.What is the size of the drop payment needed?

A)$2866.73
B)$0
C)$2810.52
D)$866.73