Deck 4: General and Other Annuities

Question 1

You deposit $5000 every year into a fund earning interest at j₂ = 7%,starting on your 30^th birthday with your final deposit made on your 65^th birthday.How much have you accumulated on your 65^th birthday? (Answer to nearest dollar)

A)$691,184
B)$709,921
C)$744,567
D)$765,485

Answer 1

$765,485

Question 2

A loan is repaid with semi-annual payments of $4500 for 10 years,first payment made six months from now.Interest on the loan is calculated at j₁ = 12%.What is the loan amount if simple interest is calculated for the fractional part of an interest period? (Answer to nearest dollar. )

A)$50,852
B)$51,615
C)$52,334
D)$52,378

Answer 2

$52,378

Question 3

Payments of $500 are made at the end of each month to a savings account paying j₄ = 10%.How much will be in the account at the end of 5 years if simple interest is used for part of a interest conversion period?

A)$38,316.98
B)$38,634.54
C)$38,636.29
D)$39,111.19

Answer 3

$38,636.29

Question 4

A couple borrows $A today at j₁ = 12%.The loan is to be repaid over 4-years with quarterly payments of $500,first payment due 3-months from today.If simple interest is credited for fractional interest periods,what is A?

A)$6280.55
B)$6341.61
C)$6348.06
D)$6530.30

Question 5

You deposit $10,000 today and withdraw $R at the end of every 6 month period for 5 years.If the interest rate is j₁ = 12%,what is R?

A)$1347.76
B)$1358.68
C)$1387.05
D)$1399.44

Question 6

An investor makes deposits of $R every 2 weeks into a fund paying interest at j₄ = 6%.At the time of the 130^th deposit,she wishes to have accumulated $50,000.What is R?

A)$326.31
B)$330.57
C)$445.23
D)$450.54

Question 7

$500 is deposited at the end of every three months into an account crediting interest at j₂ = 10%.The fund credits simple interest for fractional parts of an interest period.What is the accumulated value of the fund at the end of 3 years?

A)$6885.90
B)$3191.91
C)$6886.94
D)$3400.96

Question 8

What semi-annual payment for 5 years will pay off a loan of $5,000 with interest at j₄ = 13%,if the first payment is made 6 months from now?

A)$695.52
B)$698.97
C)$702.53
D)$706.10

Question 9

$500 is deposited at the end of every three months into an account crediting interest at j₂ = 10%.The fund credits simple interest for fractional parts of an interest period.What is the accumulated value of the fund at the end of 3 years?

A)$3191.91
B)$3400.96
C)$6885.90
D)$6886.94

Question 10

A company deposits $5000 at the end of every month into a fund that pays j₄ = 18%.What is the equivalent quarterly deposit,made at the end of every 3-month period,if the fund credits simple interest for the fractional part of an interest period?

A)$15,222.80
B)$15,225.00
C)$15,450.00
D)$15,685.13

Question 11

Gerry deposits $2000 at the end of every 3-month period in a fund earning interest at j₂ = 8%.If the fund pays simple interest for the fractional part of any interest period,what is the accumulated value of Gerry's deposits at the end of 5 years?

A)$48,984.91
B)$48,504.67
C)$48,499.97
D)$48,024.42

Question 12

Deposits of $1000 are made at the end of every half year into a fund earning interest at j₁ = 10%.The fund credits simple interest for any fractional part of an interest period.How much is in the fund at the end of 10 years?

A)$31,874.80
B)$32,652.74
C)$32,671.72
D)$33,468.54

Question 13

You deposit $R every 6 months in a fund earning interest at j₄ = 5%.Six months after your 15^th deposit,you have accumulated $8650.What is R?

A)$469.94
B)$481.83
C)$521.36
D)$527.80

Question 14

You deposit $20,000 today into a fund paying j₁ = 8%.From this fund,you receive 10 payments of $R,with the payments made at the end of 2 years,4 years,6 years,…,20 years.What is R?

A)$4942.10
B)$4912.76
C)$4237.05
D)$4138.02

Question 15

A $3000 loan is to be repaid with quarterly payments or $R over five years,first payment due 3 months from now.What is R if j₂ = 10%?

A)$191.89
B)$388.51
C)$190.84
D)$342.24

Question 16

What is the accumulated value of 10 annual deposits of $1200 immediately after the 10^th deposit,if j₄ = 10%?

A)$19,478.09
B)$19,375.62
C)$19,124.91
D)$18,972.32

Question 17

Fred deposits $50 at the end of every month for 5 years into a fund earning j₄ = 12%.What is the value of the fund one month after the final deposit?

A)$4030.56
B)$4070.60
C)$4110.90
D)$4151.47

Question 18

Gerry deposits $2000 at the end of every 3-month period in a fund earning interest at j₂ = 8%.If the fund pays simple interest for the fractional part of any interest period,what is the accumulated value of Gerry's deposits at the end of 5 years?

A)$48,024.42
B)$48,499.97
C)$48,504.67
D)$48,984.92

Question 19

A $3000 loan is to be repaid with quarterly payments or $R over five years,1^st payment due 3 months from now.What is R if j₂ = 10%?

A)$190.84
B)$191.89
C)$342.24
D)$388.51

Question 20

An investor makes deposits twice a month into a fund paying interest at j₄ = 6.5%.At the time of the 80^th deposit,she wishes to have $100,000.What deposit is needed?

A)$1121.99
B)$1131.50
C)$1379.80
D)$1391.00

Question 21

On September 1,2014,a university receives a grant of $100,000 that is invested at 8% compounded quarterly.The grant is to be used to pay out semi-annual scholarships for 20 years.What is the size of each scholarship if the first one is awarded on September 1,2016?

A)$5954.92
B)$5082.46
C)$5683.21
D)$5723.68

Question 22

Deposits of $2500 are made at the end of each 3-month period to a savings account paying j₂ = 8%.How much will be in the account at the end of 4 years if simple interest is used for the fractional part of an interest period?

A)$46,301.49
B)$46,527.33
C)$46,531.84
D)$46,992.55

Question 23

An endowment fund of $20,000 is to pay out $R every year forever,with the first payment made exactly 2 years from now.If j₁ = 7%,what is R?

A)$1308.41
B)$1400.00
C)$1498.00
D)$1602.86

Question 24

A couple has determined that they can afford to make mortgage payments of $1250 per month.If they can obtain a 25 year mortgage at j₂ = 10%,how large a mortgage can they afford to get (Answer to nearest dollar)?

A)$137,559
B)$139,745
C)$142,289
D)$375,000

Question 25

A couple takes out a mortgage for $180,000 at j₂ = 8%.They plan to make payments twice a month over 25-years.What is the size of the payment?

A)$632.94
B)$634.05
C)$685.77
D)$686.89

Question 26

A woman has bought a house and makes mortgage payments of $400 every two-weeks for 25 years.If the mortgage interest rate is j₂ = 7%,what is the size of her original mortgage loan? (Answer to nearest dollar)

A)$123,927
B)$120,104
C)$117,713
D)$114,382

Question 27

$A is invested today into a scholarship fund earning j₁ = 8%.The first scholarship (paid 1 year from now)is $1000 and each succeeding scholarship is $2000 a year.What is A? (Answer to nearest dollar)

A)$22,359
B)$24,074
C)$24,184
D)$26,000

Question 28

Jim buys a house and takes out a mortgage of $150,000 at j₂ = 6%,to be repaid over 20 years with weekly payments of R.What is the value of R?

A)$244.37
B)$246.06
C)$247.75
D)$267.07

Question 29

A mortgage of $A is obtained at a rate of j₂ = 6%.The mortgage is to be paid off with monthly payments of $700 for 25 years (first payment one month from now).What is A? (Answer to nearest dollar. )

A)$108,065
B)$108,645
C)$109,408
D)$110,302

Question 30

A couple takes out a mortgage for $135,000 at j₂ = 6%.They plan to make payments once every two weeks over 20 years to pay off the mortgage,with the first payment two weeks from now.What is the size of the payment?

A)$443.16
B)$461.01
C)$462.63
D)$480.14

Question 31

A couple buys a house and takes out a $250,000 mortgage.They plan to make payments twice a month,with the first payment one half month from now.If they choose a 25 year amortization period and j₂ = 4.2%,what is the size of their bi-monthly monthly payments?

A)$670.57
B)$667.62
C)$648.48
D)$618.94

Question 32

At age 65 a man takes his life savings of $192,000 and buys a 25-year annuity that provides him with monthly payments.What is the size of these payments if the annual interest rate is j₃₆₅ = 6%?

A)$1238.76
B)$1258.64
C)$1251.63
D)$1237.06

Question 33

You deposit $5000 every year into a fund earning interest at j₂ = 7%,starting on your 30^th birthday with your final deposit made on your 65^th birthday.How much have you accumulated on your 65^th birthday? (Answer to nearest dollar)

A)$691,184
B)$709,921
C)$744,567
D)$765,485

Question 34

A $60,000 mortgage is obtained at a rate of j₂ = 13%.The mortgage is to be paid off with weekly payments for 20 years (note: 52 weeks in a year).What is the weekly payment?

A)$172.13
B)$162.08
C)$158.25
D)$154.60

Question 35

Gerry make quarterly deposits $2,000 at the end of every 3-month period in a fund earning interest compounded semi-annually at j₂ = 8%.If the fund pays simple interest for the fractional part of any interest period,what is the accumulated value of Gerry's deposits at the end of 5 years?

A)$48,024.44
B)$48,264.56
C)$48,499.96
D)$48,504.67

Question 36

A couple buys a house for $165,000 with $45,000 as a down payment.They plan to make payments twice a month (24 payments a year),with the first payment half a month from now.If they choose a 25 year amortization period and j₂ = 8%,what is the size of their mortgage payments?

A)$457.18
B)$462.85
C)$469.22
D)$628.68

Question 37

A couple takes out a mortgage for $250,000 at j₂ = 6%.They choose a 15 year amortization period and make weekly payments of $R.What is R?

A)$396.91
B)$483.63
C)$486.26
D)$524.93

Question 38

John bought a house for $135,000,with a down payment of $20,000.He takes out a 20-year mortgage at j_{2 ­}= 8%.What is his monthly mortgage payment?

A)$ 952.61
B)$ 961.91
C)$ 1118.28
D)$ 1129.19

Question 39

You have a mortgage of $120,000 at j₂ = 5%.You wish to make payments of R every 2 weeks for 25 years to pay off the mortgage.What is R?

A)$348.60
B)$335.48
C)$323.59
D)$321.76

Question 40

A preferred stock pays a semi-annual dividend of $12 per share,with the first dividend paid 6-months from now.If j₂ = 10%,how much should a share of this stock be selling for today?

A)$117.07
B)$120.00
C)$234.15
D)$240.00

Question 41

You invest $A today.From this fund,you withdraw $500 today,followed by withdrawals that increase by 3% every 3 months.You plan to make a total of 20 quarterly withdrawals.If your investment earns interest at j₄ = 8%,what is A?

A)$10,773.05
B)$10,988.52
C)$11,096.25
D)$11,208.29

Question 42

Dave decides to donate $10,000 to UWO in order to set up scholarship fund paying $R every year forever.If the first scholarship is to be paid out immediately and if j₁ = 7%,what is R?

A)$700.00
B)$675.45
C)$654.21
D)$651.00

Question 43

A company has set aside $10,000 as an endowment in order to pay a cash award of $R every month to the "employee of the month" forever.If the first award is paid one month from now and the company can earn j₁₂ = 8.4% for the first 24 months and j₁₂ = 6% thereafter,what is R?

A)$45.04
B)$50.14
C)$52.30
D)$70.00

Question 44

Sally has just won the lottery.She is given two equivalent choices as to how the winnings will be paid.She can receive a lump sum of $A today or she can receive 20 semi-annual payments.The first payment would be $10,000 and is to be paid today,with each succeeding payment being 91% of the preceding payment [2^nd payment = 10,000(0.91)].If the interest rate is j₂ = 8%,what is the value of A?

A)$65,155.39
B)$71,599.33
C)$73,672.34
D)$74,463.30

Question 45

You make deposits at the end of every 3-months into a fund earning interest at j₄ = 8%.The first deposit is $500 and each succeeding deposit is 5% less than the preceding deposit.How much have you accumulated at the time of the 20^th deposit?

A)$5528.00
B)$7650.63
C)$8053.30
D)$8214.36

Question 46

Dave decides to donate $10,000 to UWO in order to set up scholarship fund.The first scholarship will be $R,payable one year from now,with each succeeding annual scholarship being $50 higher.If j₁ = 7%,what is R?

A)$750
B)$700
C)$650
D)Dave does not have enough money to fund this scholarship

Question 47

A scholarship fund is set up to pay out $10,000 in one year's time,with each succeeding annual scholarship being $100 higher.Annual scholarships are to continue forever.If j₁ = 10%,how much money is need to be invested today to fund this scholarship plan?

A)$100,000
B)$101,000
C)$109,091
D)$110,000

Question 48

A scholarship fund has $50,000 in it today and it earns interest at j₂ = 8%.The fund is to pay out a perpetuity of $R every 6-months,with the first payment to be made 1 year from today.What is R? (Answer to nearest dollar)

A)$2163
B)$2080
C)$2000
D)$1923

Question 49

You deposit $200 in a savings account.Each succeeding annual deposit is 3% higher.How much has been saved in your account immediately after you make your 20^th deposit if j₁ = 6%?

A)$3087.05
B)$5326.56
C)$9340.16
D)$9900.57

Question 50

An ordinary perpetuity has semi-annual payments of $R and is purchased for $25,000.It pays interest at j₂ = 9% for the first 5 years,and j₂ = 7% thereafter.What is R? (Answer to nearest dollar)

A)$875
B)$950
C)$1038
D)$1125

Question 51

An employer wants to pay $400 every 6 months to a deserving employee forever.The company has $A to fund the award and can earn j₂ = 8%.If the first award is to be paid out 3 months from now,what is A? (Answer to nearest dollar)

A)$9,806
B)$10,000
C)$10,198
D)$10,400

Question 52

If money is worth j₄ =12%,what is the present value of a perpetuity of $1000 per quarter,first payment due in exactly 6 years (Answer to nearest dollar)?

A)$16,398
B)$16,780
C)$16,890
D)$17,876

Question 53

An ordinary perpetuity has semi-annual payments of $950 and is purchased for $A.It pays interest at j₂ = 9% for the first 5 years,and j₂ = 7% thereafter.What is A? (Answer to nearest dollar)

A)$26,759
B)$34,660
C)$24,995
D)$28,589

Question 54

An employer wants to pay $400 every 6 months to a deserving employee forever.The company has $A to fund the award and can earn j₂ = 8%.If the first award is to be paid out 3 months from now,what is A? (Answer to nearest dollar)

A)$9,806
B)$10,000
C)$10,198
D)$10,400

Question 55

ACME Industries stock pays quarterly dividends of $2.25 per share,with the next payment today.If j₁ = 5%,and dividends are expected to continue forever,what is the share price?

A)$ 45.00
B)$ 45.84
C)$ 183.34
D)$ 185.59

Question 56

An alumnus sets up a scholarship at her university with a $10,000 donation.The annual scholarship will $R,with the first payment made today.What is R,if the money can be invested at j₁ = 11%? (Answer to nearest dollar)

A)$893
B)$991
C)$1100
D)$1221

Question 57

A scholarship pays $1000 at the end of first year,$1200 at the end of the second year,$1400 at the end of the third year,etc.Immediately after the 4^th scholarship payment is made,the scholarship fund is refinanced at j₁ = 4%.How much money is needed at that time to make sure the payments can continue in this fashion forever?

A)$165,000
B)$150,000
C)$160,000
D)$170,000

Question 58

You deposit $A today into a fund earning j₁ = 10%.You wish to make annual withdrawals for a total of 20 withdrawals.The first withdrawal will be $20,000 and it will be made two years from now.Each succeeding withdrawal will be 5% higher.What is the value of A? (Answer to nearest dollar)

A)$205,162
B)$220,220
C)$242,242
D)$266,466

Question 59

An investment of $81,000 pays out $1,000 per month forever,starting today.What interest rate,j₁₂,is the money invested at?

A)14.8%
B)15.0%
C)15.9%
D)16.1%

Question 60

An endowment fund is set up today.It provides payments of $1500 a year for 6-years (first payment one year from now)followed by $2000 a year thereafter forever.If the interest rate is j₁ = 6%,how much is needed to be deposited (invested)today? (Answer to nearest dollar)

A)$40,709
B)$38,889
C)$30,875
D)$29,545

Question 61

A loan of $150,000 are to be paid out monthly for 10 years,with interest at j₁₂ = 6%.The first payment,paid one month from now,is $R and each succeeding monthly payment is 1% higher than previous one.What is the value of R?

A)$931.65
B)$921.38
C)$916.79
D)$912.23

Question 62

Lottery winnings of $250,000 are to be paid out monthly for 10 years,with interest at j₁₂ = 9%.The first payment,paid one month from now,is $R and each succeeding monthly payment is 1% higher.What is the value of R?

A)$1777.76
B)$1791.10
C)$1804.53
D)$1817.54

Question 63

A man deposits $50 into a fund today.The fund pays j₄ = 6%.Three months later,he deposits $80 into the fund and every three month period after that he increases his deposit by $30 until he has made a total of 80 deposits.How much is in his fund at the time of his 80^th deposit? (Answer to nearest dollar)

A)$153,057
B)$155,353
C)$157,689
D)$157,753

Question 64

You deposit $A today in a fund paying interest at j₄ = 8%.You plan to make quarterly withdrawals for 5 years,starting 3 months from now.The first withdrawal is $500,with each succeeding withdrawal increasing by 3%.What is A?

A)$8,950.24
B)$9,129.25
C)$10,773.05
D)$10,988.52

Question 65

Charlie makes monthly deposits into an account earning j₁₂ = 6%.His first deposit is $P and each monthly deposit thereafter increases by $80.One month after his 24^th deposit,he has accumulated $36,415.What is P?

A)$530.95
B)$528.30
C)$526.44
D)$523.85

Question 66

A scholarship fund is set up with a lump sum payment of $A today.The fund will make a payment at the end of every year.The payments are: $60,$140,$220,…..If j = 8%,what is A?

A)$14,310
B)$13,250
C)$11,205
D)$10,375

Question 67

A person aged 25 will contribute 5% of his annual earnings to a pension plan.Suppose he is currently earning $60,000 per year and will get an annual raise of 3%.He is expecting to retire in 40-years at age 65.If the interest rate is j₁ = 7%,how much will he have accumulated at age 65? (Assume salary is paid in one lump sum at the end of each year.Answer to nearest dollar. )

A)$939,922
B)$878,432
C)$904,784
D)$868,930

Question 68

A scholarship fund has $50,000 in it today and it earns interest at j₂ = 8%.From this amount,you wish to pay out semi-annual scholarships of $R,first scholarship 6-months from now,and each succeeding semi-annual scholarship thereafter increases by $50 forever.What is R?

A)$750
B)$1950
C)$2000
D)$3375

Question 69

Whassamatter U.sets up a scholarship fund.The first scholarship is $1000 and is paid today,with each succeeding annual scholarship increasing by $10 a year forever.If the fund earns interest at j₁ = 10%,how much money is needed today?

A)$11,000
B)$11,100
C)$12,000
D)$12,100

Question 70

Deposits are made into an account at the end of every 2 months as follows:
600,575,550,525,… If the fund earns interest at j₆ = 6%,what is the accumulated value of this account at the end of 2 years?

A)$6262.33
B)$5962.29
C)$5903.24
D)$5622.33

Question 71

Geri Ginger deposits $A today in a fund paying interest at j₂ = 8%.She withdraws $500 six months from now and each succeeding semi-annual withdrawal is 10% higher.Withdrawals continue for 10 years in total.What is A? (Answer to nearest dollar)

A)$5,943
B)$11,971
C)$17,253
D)$17,943

Question 72

A varying annuity has 15 annual payments.The first payment is $2000,and each succeeding payment increases by 5%.What is the accumulated value of these payments immediately after the 15^th deposit if j₁ = 8%? (Answer to nearest dollar)

A)$24,814
B)$72,883
C)$78,713
D)$51,586

Question 73

A man deposits $50 into a fund today.The fund pays j₄ = 6%.Three months later,he deposits $80 into the fund and every three month period after that he increases his deposit by $30 until he has made a total of 80 deposits.How much is in his fund at the time of his 80^th deposit? (Answer to nearest dollar. )

A)$153,057
B)$155,353
C)$157,689
D)$157,753

Question 74

Jill deposits $500 in her savings account at the end of 1 month,with each succeeding deposit being $5 less.The account pays interest at j₁₂ = 6%.How much has she accumulated at the end of 7 years?

A)$21,023.20
B)$31,963.04
C)$47,429.84
D)$72,110.88

Question 75

You deposit $5000 into a fund earning j₂ = 6%.Each succeeding semi-annual deposit is increased by 4%.What is the accumulated value immediately after your 15^th deposit? (Answer to nearest dollar)

A)$96,714
B)$121,488
C)$125,133
D)$148,904

Question 76

A varying annuity has 15 annual payments.The first payment is $2000,and each succeeding payment increases by 5%.What is the accumulated value of these payments 5 years after the 15^th deposit if j₁ = 8%? (Answer to nearest dollar)

A)$63,412
B)$101,989
C)$107,089
D)$112,443

Question 77

A man makes an initial deposit of $1000.Every three months thereafter his deposits are $50 lower than the previous deposit.If j₄ = 10%,how much has he accumulated at the time of the 16^th deposit? (Answer to the nearest dollar)

A)$26,141
B)$19,380
C)$19,211
D)$12,620

Question 78

A person deposits $100 into a fund paying interest at j₄ = 6%.Each succeeding quarterly deposit is to be 2% higher.How much has been accumulated in the fund immediately after the 18^th deposit?

A)$2454.38
B)$2418.11
C)$2089.92
D)$1877.39

Question 79

You receive an inheritance of $A.You invest this money in a fund that pays j₂ = 10%.You wish to make 10 semi-annual withdrawals from this fund,first withdrawal being made today.The first withdrawal is $2000 and each subsequent withdrawal increases by $100.What is A? (Answer to nearest dollar. )

A)$21,381
B)$19,539
C)$18,828
D)$18,609