Deck 12: Ordinary General Annuities

Question 1

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each month if interest is 4% compounded semi-annually.

Answer 1

PMT = 1000.00; n = 10(12)= 120; i = = 2% = 0.02; c = = ; I/Y = 4; P/Y = 12; C/Y = 2
p = - 1 = 0.00330589
FV = 100 = $146994.41
Programmed solution:

Question 2

If a loan was repaid by semi-annual payments of $4720.00 in 6.5 years at 8.24% compounded quarterly, how much interest was paid?

Answer 2

PMT = 4720, i = 0.0824 ÷ 4 = 0.0206, n = 6.5 × 2 = 13, c = = 2
p = - 1 = 0.0416244
PVg = 4720.00 = 4720.00(9.8857467)= $46 660.74
Interest paid = 13(4720.00)- 46660.72
= 61360.00 - 46660.72 = $14 699.28

Question 3

What is the discounted value of $4760.00 paid at the end of each year for 7 years if interest is 6.52% compounded quarterly?

Answer 3

PMT = 4760, i = 0.0652 ÷ 4 = 0.0163, n = 7, c = = 4
p = - 1 = 0.0668115
PVg = 4760.00 = 4760.00(5.4497186)= $25 940.66

Question 4

What is the accumulated value after 15.50 years of deposits of $500.00 earning interest at 4.00% compounded semi-annually if the deposits are made at the end of each quarter?

Question 5

What is the accumulated value of deposits of $1120.00 made at the end of every six months for three years if interest is 8.48% compounded quarterly?

Question 6

What is the accumulated value of deposits of $2000.00 made at the end of every year for three years if interest is 6.00% compounded quarterly?

Question 7

Ralph Bogita saves $50.00 at the end of each month and deposits the money in an account, paying 3.00% compounded semi-annually.
a)How much will she accumulate in 20 years?
b)How much of the accumulated amount is interest?

Question 8

A real estate developer bought land for $170 000.00 down and monthly payments of $10 450.00 for 5 years. What is the equivalent cash price if money is worth 7.75% compounded semi-annually?

Question 9

A loan is repaid by making payments of $6000.00 at the end of every six months for twelve years. If interest on the loan is 8% compounded quarterly, what was the principal of the loan?

Question 10

A student bought a rental property for $40 000.00 down and monthly payments of $1000.00 for 5 years. What is the equivalent cash price if money is worth 5.75% compounded semi-annually?

Question 11

Mrs. Engleder has made deposits of $750.00 at the end of every six months for twenty-three years. If interest is 3.72% compounded monthly, how much will Mrs. Engleder have accumulated six years after the last deposit?

Question 12

What is the accumulated value after 11.25 years of monthly deposits of $415.00 earning interest at 5.56% compounded semi-annually if the deposits are made at the end of each month?

Question 13

What is the principal from which $279.00 can be withdrawn at the end of each month for 17.5 years if interest is 5.44% compounded quarterly?

Question 14

A 21-year mortgage is amortized by making payments of $3052.61 at the end of every three months. If interest is 8.45% compounded annually, what was the original mortgage balance?

Question 15

Conchita Martinez saves $17.25 at the end of each month and deposits the money in an account, paying 4.96% compounded quarterly.
a)How much will she accumulate in 22 years?
b)How much of the accumulated amount is interest?

Question 16

If a student loan was repaid by monthly payments of $800.00 in 5.0 years at 8.00% compounded yearly, how much interest was paid?

Question 17

What is the discounted value of $3000.00 paid at the end of every six months for 5 years if interest is 8.00% compounded yearly?

Question 18

If a loan was repaid by monthly payments of $9230.00 in 7.5 years at 6.15% compounded annually, how much interest was paid?

Question 19

What is the future value of payments of $230.00 made at the end of every three months in twenty-one years if interest is 7.65% compounded annually?

Question 20

For her daughter's university education, Carla Hackl has invested an inheritance in a fund paying 9.2% compounded quarterly. If ordinary annuity payments of $4750.00 per month are to be made out of the fund for 5 years and the annuity begins 7.75 years from now, how much was the inheritance?

Question 21

Edward Martin borrowed $15 810.00 from his uncle to finance his graduate studies. The loan agreement calls for equal payments at the end of each month for 6 years. The payments are deferred for 3 years and interest is 8.12% compounded semi-annually. What is the size of the monthly payments?

Question 22

Calculate the amount of money that must be deposited at the end of every three months into an account paying 6% compounded monthly to accumulate to $12 500.00 in ten years?

Question 23

How much must be deposited at the end of each month for 10 years to accumulate to $100 000.00 at 6.00% compounded yearly?

Question 24

You won $250 000.00 in a lottery and you want to set some of that sum of money aside for 11.5 years. After 11.5 years, you would like to receive $4500.00 at the end of each month for 4.75 years. If the interest is 6.79% compounded annually, how much of your winnings must you set aside?

Question 25

A loan of $91 450.00 is to be repaid by equal semi-annual payments for 11 years. What is the size of each semi-annual payment if the interest is 9.24% compounded annually?

Question 26

You won $150 000.00 in a lottery and you want to set some of that sum of money aside for 6 years. After 6 years you would like to receive $2710.00 at the end of every 6 months for 8 years. If interest is 6% compounded quarterly, how much of your winnings must you set aside?

Question 27

Kelsey bought a car priced at $19 700.00 for 10% down and equal monthly payments for 4.5 years. If interest is 8.22% compounded semi-annually, what is the size of the monthly payment?

Question 28

For how long will Harold have to make payments of $550.00 at the end of every three months to repay a loan of $16 900.00 if interest is 9% compounded monthly?

Question 29

A mortgage of $198 000.00 is to be amortized by payments over 22.5 years. If the payments are made at the end of each month and interest is 8.75% compounded semi-annually, what is the size of the monthly payments?

Question 30

A loan of $40 000.00 is to be repaid by equal quarterly payments for 5 years. What is the size of each semi-annual payment if the interest is 5.00% compounded annually?

Question 31

For how long will Jessica have to make payments of $1200.00 at the end of every three months to repay a loan of $10 000.00 if interest is 12% compounded semi-annually?

Question 32

A loan was repaid in 6.5 years by quarterly payments of $515.00 at 9.85% compounded semi-annually. What is the value of the loan?

Question 33

How much must be deposited at the end of each quarter for 5 years to accumulate to $27 000.00 at 6.84% compounded monthly?

Question 34

A $ 120 000.00 mortgage is amortized over 25 years. If interest on the mortgage is 8.5% compounded semi-annually, calculate the size of monthly payments made at the end of each month.

Question 35

What sum of money can be withdrawn from a fund of $46 950.00 invested at 6.5% compounded semi-annually at the end of every three months for twelve years?

Question 36

How many deposits of $6100.00 made at the end of every 6 months are needed to accumulate to $172 000.00 at 5.24% compounded quarterly?

Question 37

What is the principal invested at 6.76% compounded semi-annually from which monthly withdrawals of $450.00 can be made at the end of each month for 22 .75 years?

Question 38

How much must be contributed into an RRSP at the end of each year for 37 years to accumulate to $213 000.00 if interest is 8.04% compounded quarterly?

Question 39

Sean Paul borrowed $20 000.00 from his father to finance his new business. The loan agreement calls for equal payments at the end of each month for 10 years. The payments are deferred for 4 years and interest is 4.00% compounded semi-annually. What is the size of the monthly payments?

Question 40

A 22-year mortgage is amortized by payments of $1761.50 made at the end of each month. If interest is 9.65% compounded semi-annually, what is the mortgage principal?

Question 41

How much should you invest today into account paying 3.2% compounded quarterly if you want to be able to withdraw at the end of every 3 month the amounts of money growing at a constant rate of 3% for the period of 5 years , if the first withdrawal is to be $100 five years three months from now?

Question 42

Note: The calculations for this question were done using Excel's RATE function.
A property worth $15 000.00 is purchased for 10% down and semi-annual payments of $1750.00 for twelve years. What is the effective rate of interest if interest is compounded semi-annually?

Question 43

Calculate the accumulated value after twenty years of payments of $12 000.00 made at the end of each year if interest is 6% compounded semi-annually.

A)$445 721.73
B)$322 444.73
C)$642 766.07
D)$240 000.00
E)$441 427.09

Question 44

Note: The calculations for this question were done using Excel's RATE function.
What nominal annual rate of interest compounded semi-annually is earned by quarterly deposits of $7327.00 made for six years if the balance just after the last deposit is $289 000.00?

Question 45

Calculate the nominal interest rate of interest compounded quarterly if a loan of 43 000.00 is repaid in seven years by payments of $4000.00 made at the end of every six months.

Question 46

Note: The calculations for this question were done using Excel's RATE function.
A $345 000.00 mortgage is repaid in 19 years by making monthly payments of $2486.44. What is the nominal annual rate of interest compounded semi-annually?

Question 47

Calculate the accumulated value after ten years of payments of $1000.00 made at the end of each year if interest is 6% compounded monthly.

A)$10 228.03
B)$13 285.11
C)$10 228.56
D)$10 600.00
E)$13 228.03

Question 48

For how long must $179.23 be deposited at the end of each month to accumulate to $9700.00 at 6.18% compounded quarterly?

Question 49

Deon makes monthly contributions of $250.00 at the end of every month into an RRSP. Calculate, to the nearest month, how long it will take to grow to $100 000.00 if interest is 8% compounded annually.

Question 50

A loan of $54 000.00 is repaid by making payments of $3000.00 at the end of every three months. If the interest is 9% compounded monthly, calculate how long the payments have to be made.

Question 51

Note: The calculations for this question were done using Excel's RATE function.
What is the rate of interest compounded quarterly if a loan of $31 500.00 is repaid in seven years by payments of $2712.00 made at the end of every six months?

Question 52

What is the final amount of an investment where you are making quarterly deposits of $672.31 at the end of the payment period for 7 years and 9 months? The interest rate is 6.16% compounded semi-annually.

A)$26 811.16
B)$28 611.16
C)$26 611.57
D)$28 811.16
E)$26 407.57

Question 53

Mr. Lavergne accumulated $320 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $7500.00 at the end of every three months from the fund. If interest is 4.68% compounded monthly, how many withdrawals can Mr. Lavergne make?

Question 54

A $360 000.00 mortgage is amortized by making monthly payments of $2600. If interest is 7.5% compounded semi-annually, what is the term of the mortgage?

Question 55

Note: The calculations for this question were done using Excel's RATE function.
A $160 000.00 mortgage with a 20-year term is repaid by making monthly payments of $1361.00. What is the rate of interest compounded semi-annually on the mortgage?

Question 56

Sabrina deposits $300.00 into a savings account at the end of each month for five years. If the accumulated value of the deposits is $20 000.00 and interest is compounded semi-annually, calculate the nominal rate of interest

Question 57

Note: The calculations for this question were done using Excel's RATE function.
Compute the nominal annual rate of interest on a loan of $67 000.00 repaid in semi-annual installments of $6540.00 in 11.5 years.

Question 58

You miss the 11th to 13th payments of a loan. The loan payments are $519.27 each month and the interest rate is 8.45% compounded annually. How much are you behind in your payments on the day that you miss the 13th payment?

A)$1658.40
B)$1586.40
C)$1568.40
D)$1508.40
E)$1458.40

Question 59

Mr. Sepaba accumulated $600 000.00 in an RRSP. He converted the RRSP into an RRIF and started to withdraw $3000.00 at the end of every month from the fund. If interest is 4.5% compounded yearly, for how long can Mr. Sepaba make withdrawals?

Question 60

For their daughter's future education David and Bonnie set a fund in which they invest at the end of every six months. The first investment is $100 and they plan to increase their investments at a constant rate of 0.5%. If the fund earns 2 .4% compounded semi-annually, how much money will be in the fund in 16 years when their daughter goes to college?

Question 61

You make 4 semi-annual deposits starting at $350 and increasing at a constant rate of 2.14%. The interest rate is 5.12% compounded annually. How much has been deposited in total?

A)$1445.59
B)$1454.59
C)$1400.00
D)$1459.59
E)$1444.59

Question 62

A mortgage requires payments of $1000.00 at the end of every month for twenty-five years. If interest is 6% compounded semi-annually, calculate the principal of the loan.

A)$156 297.23
B)$155 206.86
C)$46 188.41
D)$300 000.00
E)$33 328.64

Question 63

You buy a motorcycle for $52 523 plus freight of $724 and other delivery charges of $561. You have saved 25% of the total purchase price towards a down payment. The bank is willing to finance the purchase of the motorcycle at 9.86% compounded quarterly. What is the size of your monthly payment if the loan is for 4.5 years?

A)$296.80
B)$926.80
C)$962.80
D)$996.80
E)$262.80

Question 64

You can buy a piece of equipment for $8600. The equipment is expected to last for 9 years and you want to have it completely paid off 3.5 years before it becomes unusable. Current loan rates are 9.5% compounded annually. What is the size of your semi-annual payment?

A)$1515.98
B)$1105.98
C)$1055.98
D)$1015.98
E)$1115.98

Question 65

What is the payment size of a loan that has semi-annual payments and an interest rate of 5.52% compounded monthly? The loan principal is $1641.12 and the loan is for 48 months.

A)$321.74
B)$231.74
C)$123.74
D)$274.31
E)$221.31

Question 66

Mark deposits $900 at the end of each month in a savings account earning 4.5% quarterly. How soon can he buy his first car assuming that he needs $8 000 for a decent car.

A)8.76 months
B)8.52 months
C)9.06 months
D)9 years
E)8.86 months

Question 67

You make 6 quarterly deposits starting at $135 and increasing at a constant rate of 4.5%. The interest rate is 8.4% compounded quarterly. What is the size of the last deposit?

A)$186.23
B)$168.23
C)$128.63
D)$135.00
E)$668.23

Question 68

You lease a car for monthly payments of $610.23 at the end of each month for 54 months. There is a no security deposit sale going on. The interest rate on the lease is 3.9% compounded annually. The buy-out is $19552 at the end of the lease. How expensive is the vehicle?

A)$48 683.26
B)$48 863.26
C)$46 683.26
D)$46 863.26
E)$48 633.26

Question 69

Saba gets a year-end bonus in December every year before the Christmas. She plans to invest $1000 from the bonus at the end of every year into mutual funds RRSP, which are expected to grow at the rate of 8% compounded semi-annually. What will be the total value of her periodic investments after 25 years?

Question 70

A mortgage requires payments of $4000.00 at the end of every six months for twelve years. If interest is 8% compounded quarterly, calculate the principal of the loan.

A)$75 655.70
B)$84 948.26
C)$60 738.85
D)$88 320.00
E)none of the above

Question 71

You are to receive $16 700 from your trust fund in 7.5 years. You negotiate a deal where you can withdraw $350 per month starting 2.75 years before you can withdraw the remainder of the funds. You are able earn 4.18% compounded annually on your money. How much is your trust fund reduced to?

A)$4195.40
B)$4159.40
C)$4459.40
D)$4495.40
E)$4155.40

Question 72

Don turned 60 years old today and has retired from Hydro One. Current economic value of his pension is his significant asset. He will be receiving pension payments of $7000 at the end of each month. Based on a 22-year life expectancy and money worth 8% compounded semi-annually, calculate the current economic value of Don's pension.

Question 73

A mortgage of $326 000 is to be repaid by making payments of $2500 at the end of each month. If interest is 4.75% compounded semi-annually, what is the term of the mortgage?

A)183 months
B)106 months
C)182 months
D)184 months
E)105 months

Question 74

Calculate the amount of money that must be deposited at the end of every month into an account paying 12% compounded annually to accumulate to $100 000.00 in ten years.

A)$434.71
B)$450.59
C)$833.33
D)$45.06
E)$416.67

Question 75

A series of payments of $900 are being made at the end of each year for the next 8 years. What is the future value 8 years from now, if money can earn 9% compounded semi-annually?

A)$9999
B)$30 220
C)$77 200
D)$14 346
E)$7200

Question 76

The loan will have a term of 54 months and monthly payments of $385.13. The interest rate on the loan is 8.84% compounded quarterly. What is the amount of money that was borrowed?

A)$17 310.71
B)$17 430.71
C)$17 030.71
D)$17 130.71
E)$20 368.27

Question 77

Bhamani is contributing to a RESP they have set up for their grandchildren. What amount will they have in the RESP after 13 years of contributing $185 at the end of every month if the plan earns 5.5% compounded quarterly?

Question 78

Calculate the amount of money that must be deposited at the end of every three months into an account paying 6% compounded monthly to accumulate to $12 500.00 in ten years.

A)$293.75
B)$80.77
C)$304.94
D)$229.97
E)none of the above

Question 79

A dealer sold a car to Kristy for $2000 down and monthly payments of $259.50 for 3.5 years, including interest at 7.5% compounded annually. What was the selling price of the car?

A)$9600
B)$11 600
C)$6012.50
D)$12 899
E)$10 899

Question 80

Silva is contemplating to buy a 20 year annuity paying $2500 at the end of each month. What amount will be required to purchase the annuity, if the annuity provides a return of 6.75% compounded annually?

A)$334 000
B)$47 246
C)$600 000
D)$37 037
E)$567 436