Deck 11: Ordinary Simple Annuities

Question 1

Annette bought a vacation property for $22900.00 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?

Answer 1

a) PVn = 1224.51 = 1224.51(18.7014044)
= 22 900.06
Purchase price = 22 900.06+ 22900.00
= $45800.06
b) Interest = 24(1224.51) - 22900.06 = 29388.24 - 22900.06 = $6488.18

Question 2

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 2

PVn = 2700.00 = 2700.00(22.2084332) = $59962.77
Interest = 2700.00(40) - 59962.71 = 108000.00 - 59962.77 = $48037.23

Question 3

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?

Answer 3

FVn = 47.00 = 47.00(124.7277964) = $5862.21

Question 4

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 5

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

Question 6

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 7

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 8

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

Question 9

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 10

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 11

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?

Question 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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 20

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?

Question 21

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 22

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 23

The Savoias bought an investment property valued at $160000.00 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 24

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 25

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 26

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 27

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 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

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 30

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 31

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 32

What payment is required at the end of each month for 5 years to repay a loan of $20000.00 at 6.0% compounded monthly?

Question 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

How many semi-annually payments will it take for $500.00 deposited at the end of each half year to amount to $10000.00 at 6% compounded semi-annually?

Question 42

In what period of time could you pay back a loan of $13900.00 by making monthly payments of $296.00 if interest is 6.5% compounded monthly?

Question 43

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 44

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 45

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 46

What is the nominal rate of interest if a six-year loan of $71000.00 is repaid by monthly payments of $1701.58?

Question 47

$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 48

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 49

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 50

A $15000.00 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

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 52

How many yearly payments will it take for $25000.00 deposited at the end of each year to amount to $1000 000.00 at 9% compounded yearly?

Question 53

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 54

How many monthly payments will it take for $1000.00 deposited at the end of each month to amount to $50000.00 at 9% compounded monthly?

Question 55

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 56

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 57

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

Question 58

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 59

How many quarterly payments will it take for $400.00 deposited at the end of each quarter to amount to $11453.40 at 6% compounded quarterly?

Question 60

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 61

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 62

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) $44020.00
B) $75999.79
C) $75399.79
D) $27501.82
E) $79999.79

Question 63

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

Question 64

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 65

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 66

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 67

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) $45315.20
C) $2849.74
D) $46309.57
E) $45555.20

Question 68

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) $60616.68
B) $60161.68
C) $60186.68
D) $60611.68
E) $60001.68

Question 69

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 70

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 71

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 72

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 73

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 74

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 75

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 76

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