Deck 11: Ordinary Simple Annuities

Question 1

Randy bought an annuity to pay him $2700.00 at the end of every six months for twenty years. How much of the total annuity payments is interest, if interest is 6.5% p.a. compounded semi-annually?

Answer 1

PV_n = 2700.00 = 2700.00(22.2084332) = $59 962.77
Interest = 2700.00(40) - 59962.71 = 108000.00 - 59962.77 = $48 037.23

Question 2

Mr. and Mrs. Fox have each contributed $1825.00 per year for the last eight years into RRSP accounts earning 6.93% compounded annually. Suppose they leave their accumulated contributions for another five years in the RRSP at the same rate of interest.
a) How much will Mr. and Mrs. Fox have in total in their RRSP accounts?
b) How much did the Fox's contribute?
c) How much will be interest?

Answer 2

a) FV_n = 3650.00 = 3650.00(10.2339355) = $37 354.00
b) Contribution = 8(3650.00) = $29 200.00
c) Interest = 52219.77 - 29200.00 = $23 019.77

Question 3

The Olfert Contractors, Inc., are saving $958.00 every month in order to purchase a new paving machine in twelve years. Their savings certificates pay 6% p.a. compounded monthly. How much of the maturity value will be interest?

Answer 3

FV_n = 958.00 = 958.00(210.1501631) = 201 323.86

Question 4

Find the amount to which semi-annual deposits of $200.00 will grow in four years at 6.6% p.a. compounded semi-annually.

Question 5

Annette bought a vacation property for $22 900.00 down and quarterly mortgage payments of $1224.51 at the end of each quarter for six years. Interest is 8.4% compounded quarterly.
a) What was the purchase price of the property?
b) How much interest will Annette pay?

Question 6

How much interest is included in the accumulated value of $4750 paid at the end of every six months for 4.5 years if the interest rate is 8.5% compounded semi-annually?

Question 7

Find the present value of ordinary semi-annual payments of $810.00 for five years at 5.45% p.a., compounded semi-annually.

Question 8

Jason deposited $100.00 at the end of each month for five years into an account paying 6% compounded monthly. What will be the balance in the account at the end of the five-year term?

Question 9

What is the discounted value of deposits of $150.00 made at the end of each month for fourteen years if interest is 4.5% compounded monthly?

Question 10

How much interest is included in the accumulated value of $250 paid at the end of every month for 5 years if the interest rate is 4.0% compounded monthly?

Question 11

If a loan was repaid by ordinary monthly payments of $715.00 in seven years at 9.12%, compounded monthly, how much interest was paid?

Question 12

An installment contract for the purchase of a car requires payments of $570.60 at the end of each month for the next three years. Suppose interest is 11.8% p.a. compounded monthly.
a) What is the amount financed?
b) How much is the interest cost?

Question 13

Mr. Hughes has contributed $4000.00 per year for the last ten years into a RRSP account earning 9.00% compounded annually. Suppose he leaves the accumulated contributions for another five years in the RRSP at the same rate of interest.
a) How much will Mr. Hughes have in total in his RRSP account?
b) How much did Mr. hughes contribute?
c) How much will be interest?

Question 14

To what will deposits of $47.00 made at the end of each month amount to after seven years if interest is 10.8% compounded monthly?

Question 15

For the last four years Joe Thiesman has made deposits of $300.00 at the end of every six months earning interest at 5.7% compounded semi-annually. If he leaves the accumulated balance for another ten years at 3.2% compounded quarterly, what will the balance be in Joe's account?

Question 16

Find the present value for payments of $500.00 made at the end of each quarter for ten years, if interest is 8% compounded quarterly.

Question 17

Find the amount to which monthly deposits of $100.00 will grow in five years at 4.8% p.a. compounded monthly.

Question 18

A man put aside $5710.00 at the end of every 3 months for seven years. How much will he have six years after the least deposit, if his account earned 5.6% p.a. compounded quarterly?

Question 19

Leanne Simon made ordinary annuity payments of $81.00 per month for fourteen years earning 9% compounded monthly. How much interest is included in the future value of the annuity?

Question 20

An installment contract for the purchase of a computer requires payments of $30.00 at the end of each month for the next three years. Suppose interest is 18.00% p.a. compounded monthly.
a) What is the amount financed?
b) How much is the interest cost?

Question 21

A trust fund is set up to make payments of $1320.00 at the end of each month for seven years. Interest on the fund is 7.28% compounded monthly.
a) How much money must be deposited into the fund?
b) How much will be paid out of the fund?
c) How much interest is earned by the fund?

Question 22

What is the size of semi-annual deposits that will accumulate to $113 200.00 after 9.5 years at 6.5% compounded semi-annually?

Question 23

Planning for their child's college education, Sean and Jessica opened an account paying 8.00% compounded yearly. If ordinary annuity payments of $15 000.00 per year are to be paid out of the account for three years starting sixteen years from now, how much did the couple deposit?

Question 24

Planning for their child's college education, David and Carol Roberts opened an account paying 6.36% compounded monthly. If ordinary annuity payments of $700.00 per month are to be paid out of the account for three years starting seven years from now, how much did the Roberts' deposit?

Question 25

The Savoias bought an investment property valued at $160 000.00 by paying 25% down and mortgaging the balance over 25 years through equal monthly payments at 6% compounded monthly. What was the size of the monthly payments?

Question 26

If a loan was repaid by ordinary yearly payments of $2000.00 in five years at 9.00%, compounded yearly, how much interest was paid?

Question 27

Janice plans to retire in 10 years and would like to receive $3000.00 per month for fifteen years starting at the end of the first month after her retirement. Calculate the amount she must invest now if interest is 7.5% compounded monthly.

Question 28

What payment made at the end of each month for 13 years will amount to $17 520.00 at 9.66% compounded monthly?

Question 29

You have inherited some money and you want to set some of that money aside for ten years. After ten years, you would like to receive $7600.00 at the end of each 6 months for nine years. If the interest is 6.5% compounded semi-annually, how much of your inheritance must you set aside?

Question 30

What is the size of end-of-month monthly deposits which will accumulate to $122 200.00 after six years if interest is 5.7% compounded monthly?

Question 31

Kam expects to retire in 22 years. Beginning one month after his retirement he would like to receive $590.00 per month for 25 years. How much must he deposit into a fund today to be able to do so if the rate of interest on the deposit is 6.12% compounded monthly?

Question 32

Doris purchased a piano with $1300.00 down and monthly payments of $214.00 for two years at 9.72% compounded monthly. What was the purchase price of the piano?

Question 33

The Chretiens bought a rental property valued at $125 000.00 by paying 25% down and mortgaging the balance over 21.5 years through equal payments at the end of each quarter at 8.6% compounded quarterly. What was the size of the quarterly payments?

Question 34

If a loan was repaid by quarterly payments of $715.00 over 7 years at 8.36% compounded quarterly, how much money had been borrowed?

Question 35

What payment is required at the end of each month for 3 years to repay a loan of $8000.00 at 6.4% compounded monthly?

Question 36

What payment is required at the end of each month for 5 years to repay a loan of $20 000.00 at 6.0% compounded monthly?

Question 37

A loan was repaid in 7.25 years by end-of month monthly payments of $472. If interest was 6.12% compounded monthly, how much interest was paid?

Question 38

A father wants to provide an annuity of $3350.00 payable at the end of each 6 months during the three years his son attends college. It will be six years before his son goes to college. What single deposit must he make today that will finance the annuity, if he can invest his money at 7.84% p.a. compounded semi-annually?

Question 39

Yankee Construction agreed to lease payments of $762.79 on construction equipment to be made at the end of each month for six years. Financing is at 15% compounded monthly.
a) What is the value of the original lease contract?
b) If, due to delays, the first eight payments were deferred, how much money would be needed after nine months to bring the lease payments up to date?
c) How much money would be required to pay off the lease after nine months?
d) If the lease were paid off after nine months, what would the total interest be?
e) How much of the total interest would be due to deferring the first eight payments?

Question 40

A car was purchased for $4500.00 down and payments of $375.00 at the end of each month for 5 years. Interest is 9.72% compounded monthly.
a) What was the purchase price of the car?
b) How much will be the amount of interest paid?

Question 41

Note: The calculations for this question were done using Excel's RATE function.
What nominal rate of interest is paid on quarterly RRSP contributions of $573.00 made for 17.75 years if the balance just after the last contribution is $106 000.00?

Question 42

What is the nominal rate of interest if a six-year loan of $71 000.00 is repaid by monthly payments of $1701.58?

Question 43

Note: The calculations for this question were done using Excel's RATE function.
What is the effective annual rate of interest on a loan of $9200.00 repaid in semi-annual installments of $810.00 in nine years?

Question 44

What nominal rate of interest is earned by monthly deposits of $560.00 made for 6 years if the balance just after the last deposit is $52 700.00?

Question 45

Note: The calculations for this question were done using Excel's RATE function.
A property worth $191 000.00 can be purchased for 15% down and quarterly mortgage payments of $1972.00 for 30 years. What effective rate of interest is charged?

Question 46

Suppose $726.56 is deposited at the end of every six months into an account earning 6.45% compounded semi-annually. If the balance in the account four years after the last deposit is to be $31 300.00, how many deposits are needed?

Question 47

How many yearly payments will it take for $25 000.00 deposited at the end of each year to amount to $1 000 000.00 at 9% compounded yearly?

Question 48

$1000.00 is deposited at the end of every month into an account earning 6.00% compounded monthly. If the balance in the account five years after the last deposit is to be $50 000.00, how many deposits are needed?

Question 49

What is the term of a mortgage of $235 000.00 repaid by monthly payments of $2475.00 if interest is 7.55% compounded monthly?

Question 50

A $15 000.00 loan requires payments at the end of each month for five years. If the interest rate on the loan is 12% compounded monthly, calculate the size of each payment.

Question 51

What is the nominal rate of interest on a loan of $6800.00 repaid in semi-annual installments of $1175.00 in six years?

Question 52

In what period of time could you pay back a loan of $13 900.00 by making monthly payments of $296.00 if interest is 6.5% compounded monthly?

Question 53

How many quarterly payments will it take for $400.00 deposited at the end of each quarter to amount to $11 453.40 at 6% compounded quarterly?

Question 54

Compute the nominal annual rate of interest (compounded monthly) at which $200.00 deposited at the end of each month for ten years will amount to $30 000.00.

Question 55

Bonny converted an RRSP balance of $176 875.67 into an RRIF that will pay her $2720.00 at the end of every month for 8 years. What is the nominal rate of interest?

Question 56

What deposit made at the end of each quarter will accumulate to $20 000.00 in four years at 4% compounded quarterly?

Question 57

A loan of $19 850.00 is to be repaid in quarterly payments of $620.00. How many payments are required to repay the loan at 6.5% compounded quarterly?

Question 58

How many semi-annually payments will it take for $500.00 deposited at the end of each half year to amount to $10 000.00 at 6% compounded semi-annually?

Question 59

How many monthly payments will it take for $1000.00 deposited at the end of each month to amount to $50 000.00 at 9% compounded monthly?

Question 60

A $5000.00 loan requires payments at the end of each quarter for five years. If the interest rate on the loan is 8% compounded quarterly, calculate the size of each payment.

Question 61

You currently have $4000 saved towards the purchase of a new car. You want to be able to buy a car for $15000 in 4 years. Your money is earning 5% compounded yearly. What is the size of your yearly deposit?

A) $928.05
B) $2320.12
C) $2552.13
D) $2352.13
E) $2000.99

Question 62

You currently have $4541 saved towards the purchase of a home theatre system. You want to be able to buy a system for $6225 plus GST in 4 years. Your money is earning 4.84% compounded monthly. What is the size of your monthly deposit?

A) $12.80
B) $28.80
C) $22.80
D) $13.55
E) $20.80

Question 63

Calculate the accumulated value of quarterly payments of $100.00 made at the end of each quarter for ten years just after the last payment has been made if interest is 8% p.a. compounded quarterly.

A) $4003.91
B) $6040.20
C) $2040.00
D) $4415.88
E) $2015.88

Question 64

Regular contributions of $200 are made at the end of each month for five years into a savings account earning interest at 4% compounded quarterly. The annuity can be classified as

A) ordinary general annuity
B) ordinary annuity due
C) ordinary simple annuity
D) perpetuity
E) this is not an annuity

Question 65

Sofia plans to save for next two years. She plans to put away $1000 every 6 months starting 6 months from now. What will be the value of her savings after two years if her savings accounts earns at a rate of 8% compounded semi-annually?

A) $4000
B) $4246.46
C) $2080
D) $6414.51
E) $6632.98

Question 66

Salem plans to deposit $2200 every 6 months for 15 years to save for his son's higher education. The rate of return will be 4% compounded semi-annually for the first 5 years and 8% compounded semi-annually for the subsequent 10 years. Calculate the future value of this simple annuity, if he stops payment after 5 years.

A) $24 089.39
B) $52 782.81
C) $53 454.21
D) $106 237.02
E) $118 293.81

Question 67

When the conversion period is different from the payment period, an annuity is called:

A) ordinary
B) certain
C) general
D) deferred
E) simple

Question 68

Calculate the present value of five payments of $1500.00 made at the end of each of five consecutive years respectively if money is worth 6% compounded annually.

A) $7950.00
B) $7486.52
C) $7050.00
D) $6318.55
E) $7486.00

Question 69

You are offered payments of $475 at the end of each semi-annual period for 6.5 years. You think that the cost of money is 6.14% compounded semi-annually. What is the present cash value?

A) $5092.06
B) $5029.06
C) $5209.06
D) $5292.06
E) $5290.06

Question 70

Charter has been contributing $900 at the end of each month for the past 15 months to a savings plan that earns 4% compounded monthly. What amount will he have one year from now, if he continues with the plan?

A) $25 382.84
B) $13 819.60
C) $6898.05
D) $12 669.42
E) $13 500

Question 71

Calculate the accumulated value of monthly payments of $100.00 made at the end of each month for ten years just after the last payment has been made if interest is 12% p.a. compounded monthly.

A) $23 003.87
B) $33 003.87
C) $12 000
D) $1 046.22
E) $330 003.87

Question 72

An annuity due is an annuity for which

A) the payments are made at the beginning of each payment period
B) the payments are made at the end of each payment period
C) the payment period is not the same as the conversion period
D) the payments are made to repay a loan
E) the payments continue forever

Question 73

An annuity with periodic payments made at the end of each payment period is called:

A) ordinary
B) simple
C) annuity due
D) general
E) none of the above

Question 74

The term of annuity is

A) the interval between the first and the last payments
B) the length of the payment interval
C) the length of time from the beginning of the first payment interval to the end of the last payment interval
D) the length of the conversion interval
E) the length of time between the successive payments

Question 75

Calculate the present value of 120 payments of $50.00 made at the end of each of 120 consecutive months respectively if money is worth 12% compounded monthly.

A) $3485.03
B) $3485.02
C) $6000.00
D) $3000.00
E) $34 850.30

Question 76

What is the future value of an annuity with monthly deposits of $277 for a period of 11.5 years at an interest rate of 7.44% compounded monthly? The deposits are made at the end of the month.

A) $60 616.68
B) $60 161.68
C) $60 186.68
D) $60 611.68
E) $60 001.68

Question 77

Salem plans to deposit $2200 every 6 months for 15 years to save for his son's higher education. The rate of return will be 4% compounded semi-annually for the first 5 years and 8% compounded semi-annually for the subsequent 10 years. Calculate the future value of this simple annuity.

A) $24 089.39
B) $52 782.81
C) $53 454.21
D) $106 237.02
E) $118 293.81

Question 78

You want to save $710 per quarter for 15.5 years towards the purchase of a motor home. You think that you can earn 6.56% compounded quarterly for this period of time. If your first deposit is in 3 months, what is the most expensive motor home that you will be able to purchase?

A) $44 020.00
B) $75 999.79
C) $75 399.79
D) $27 501.82
E) $79 999.79

Question 79

You want to be able to travel and withdraw $3750 at the end of every month during your yearlong trip. During your trip your travel fund will earn 6.24% compounded monthly. What is the size of your travel fund if you want to be able to start your trip in 4 years and 7 months?

A) $32 715.58
B) $45 315.20
C) $2849.74
D) $46 309.57
E) $45 555.20

Question 80

How long will it take for quarterly deposits of $425 to accumulate to be $16440 at an interest rate of 8.48% compounded quarterly? (Final answer in years and months e.g., 7 years and 4.24 months)

A) 7 years 1.64 months
B) 7 years .136 months
C) 7 years 6.14 months
D) 28 years .55 months
E) 28 years .64 months