Deck 13: Annuities Due, Deferred Annuities, and Perpetuities

Question 1

Roxanne contributes $167.00 at the beginning of every six months into an RRSP paying interest at 8.9% compounded semi-annually.
a)How much will her RRSP deposits amount to in 31.5 years?
b)How much of the amount will be interest?

Answer 1

a)FV (due)= 167 (1.0445)
= 167(326.5655028)(1.0445)
= $56963.31
b)Total deposits = (167)× 63 = $10 521
Interest = 56963.31 - 10521 = $46 442.31

Question 2

What is the discounted value of deposits of $250.00 made at the beginning of every three months for 10.5 years if money is worth 6% compounded quarterly?

Answer 2

PV (due)= 250 (1.015)
= 250(30.99405004)(1.015)
= $7864.74

Question 3

A contract valued at 60 000.00 requires payments of $3000.00 at the beginning of each quarter. If interest is 6% compounded quarterly, calculate the term of the contract.

Answer 3

PMT = 3000.00; PV = 60 000; i = = 0.015; I/Y = 6; P/Y = C/Y = 4
60000 = 3000(1.015) 0.295566502 = 1 - -n ln 1.015 = ln 0.704433498
-n(0.014888612)= -0.350361349
n = 23.53216923 quarters ÷ 4 = 5.88 ≈6 years
Programmed solution:

Question 4

What semi-annual payment must be made into a fund at the beginning of every six months to accumulate to $4800.00 in ten years at 7% compounded semi-annually?

Question 5

The monthly rent payment on computer equipment is $30.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 12% compounded monthly?

Question 6

Determine the accumulated value after 13.5 years of deposits of $470.00 made at the beginning of every three months and earning interest at 7.2% compounded quarterly.

Question 7

Payments of $1000.00 are made into a fund at the beginning of every month for 10 years. If the fund earns interest at 12% compounded monthly, what will the balance in the fund at the end of the term?

Question 8

Hector makes payments of $2000.00 into an RRSP at the beginning of every six months starting today for 33 years. If the interest rate is 8% compounded semi-annually, calculate the accumulated value.

Question 9

What is the discounted value of deposits of $570.00 made at the beginning of every three months for 8.25 years if money is worth 8.4% compounded quarterly?

Question 10

Payments of $500.00 are made at the beginning of each month for four years. The interest rate is 4.5% compounded monthly. If no further deposits are made
a)Calculate the accumulated value twelve years after the first deposit.
b)Calculate the amount deposited.
c)Calculate the interest.

Question 11

A lease agreement valued at $15 000.00 requires payment of $900.00 at the beginning of every quarter for five years. What is the nominal rate of interest charged (compounded quarterly)?

Question 12

Determine the accumulated value after 15 years of deposits of $9000.00 made at the beginning of every three months and earning interest at 8% compounded quarterly.

Question 13

Judy paid for a living room suite over time, signing an installment contract that requires semi-annual payments of $2560.00 for 8.5 years. The first payment is made on the signing date and interest is 14.5% compounded semi-annually. What was the cash price?

Question 14

Robert Downey deposited $610.00 in a trust account on the day of his son's birth and every three months thereafter. If interest paid is 7.2% compounded quarterly, what will the balance in the trust account be before the deposit is made on the son's twenty-first birthday?

Question 15

Calculate the present value of payments of $100.00 made at the beginning of each quarter for ten years if the interest is 6% compounded quarterly.

Question 16

Payments of $845.00 are made into a fund at the beginning of every month for 5.25 years. If the fund earns interest at 8.4% compounded monthly, what will the balance in the fund be after 5.25 years?

Question 17

How much does a depositor have to save at the beginning of every three months for 15 years to accumulate $200 000.00 if interest is 4% compounded quarterly?

Question 18

The monthly rent payment on photo copier equipment is $671.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 6.84% compounded monthly?

Question 19

Linda contributes $3000.00 at the beginning of every six months into an RRSP paying interest at 6% compounded semi-annually.
a)How much will her RRSP deposits amount to in 15 years?
b)How much of the amount will be interest?

Question 20

Jessica bought a bedroom suite on credit, signing an installment contract with a finance company that requires monthly payments of $100.00 for 5 years. The first payment is made on the date of signing and interest is 24% compounded monthly.
a)What was the cash price?
b)How much will Tricia pay in total?
c)How much of what she pays will be interest?

Question 21

Tricia bought a living-room suite on credit, signing an installment contract with a finance company that requires monthly payments of $167.25 for 4.5 years. The first payment is made on the date of signing and interest is 28.8% compounded monthly.
a)What was the cash price?
b)How much will Tricia pay in total?
c)How much of what she pays will be interest?

Question 22

A sum of money is deposited at the beginning of each year for 3 years at 12% compounded annually. After the last deposit interest for the account is to be 8.24% compounded quarterly and the account is to be paid out by payments of $370.00, made at the beginning of each quarter for nine years. What is the size of the annual deposit?

Question 23

Vicki paid for a kitchen set over time, signing an installment contract that requires semi-annual payments of $500.00 for 5 years. The first payment is made on the signing date and interest is 18% compounded semi-annually. What was the cash price?

Question 24

How much does a depositor have to save at the beginning of every three months for 13.25 years to accumulate $41 600.00 if interest is 8% compounded quarterly?

Question 25

A contract valued at $81 500.00 requires payment of $3350.00 at the beginning of every six months. If interest is 6.5% compounded semi-annually, what is the term of the contract?

Question 26

Sean Paul makes deposits of $500.00 at the beginning of every three months. Interest earned by the deposits is 8% compounded quarterly.
a)What will the balance in Sean's account be after ten years?
b)How much of the balance will Sean have contributed?
c)How much of the balance is interest?

Question 27

Jack Chen makes deposits of $415.00 at the beginning of every three months. Interest earned by the deposits is 4.12% compounded quarterly.
a)What will the balance in Jack's account be after eight years?
b)How much of the balance will Jack have contributed?
c)How much of the balance is interest?

Question 28

How much does a depositor have to save at the beginning of every 6 months for eleven years to accumulate $17 448.00 if interest is 6.25% compounded semi-annually?

Question 29

Equal sums of money are withdrawn monthly from a fund of $33 000.00 for 15.25 years. If interest is 9% compounded monthly, what is the size of each withdrawal if the withdrawal is made at the beginning of each month?

Question 30

Robert Bernard deposited $1000.00 in a trust account on the day of his son's birth and every three months thereafter. If interest paid is 8% compounded quarterly, what will the balance in the trust account be before the deposit is made on the son's twenty-first birthday?

Question 31

Kelly is saving $1600.00 at the beginning of each month. How soon can he retire if he wants to have a retirement fund of $345 000.00 and interest is 11.04% compounded monthly?

Question 32

How many months will it take to accumulate $17 897.20 at 5.87% compounded semi-annually, if $1140.00 is deposited in an account at the beginning of every 6 months?

Question 33

What deposit made at the beginning of each month will accumulate to $36 000.00 at 5% compounded quarterly at the end of eight years?

Question 34

Equal sums of money are withdrawn monthly from a fund of $60 000.00 for 15 years. If interest is 12% compounded monthly, what is the size of each withdrawal if the withdrawal is made at the beginning of each month?

Question 35

Determine the future value and the present value of monthly payments of $200.00 each for five years at 12% compounded monthly if
a)the payments form an annuity due;
b)the payments form an ordinary annuity.

Question 36

Gibran bought a boat valued at $110 194.00 on the installment plan. He made equal semi-annual payments for 6 years. If the first payment is due on the date of purchase and interest is 7.5% compounded semi-annually, what is the size of the semi-annual payments?

Question 37

How much does a depositor have to save at the beginning of every 6 months for twenty years to accumulate $1 000 000.00 if interest is 6.00% compounded semi-annually?

Question 38

Determine the future value and the present value of monthly payments of $173.00 each for six years at 6.48% compounded monthly if
a)the payments form an annuity due;
b)the payments form an ordinary annuity.

Question 39

What is the accumulated value after 15 years of monthly deposits of $500.00 earning interest at 8% compounded semi-annually if the deposits are made
a)at the end of each month?
b)at the beginning of each month?

Question 40

A lease requires payments of $1200.00 at the beginning of every quarter for ten years. If interest is 6% compounded monthly, calculate the value of the lease.

Question 41

Bow Valley Credit Union entered a lease contract valued at $3100.00. The contract provides for payments at the beginning of each month for three years. If interest is 8.8% compounded quarterly, what is the size of the monthly payment?

Question 42

Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually. Seven years after the last contribution, Amy converted the RRSP into an RRIF that is to pay her equal quarterly amounts for 17.25 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 7.66% compounded quarterly, how much will Amy receive every three months?

Question 43

Gary and Sandra Duncan bought a property by making semi-annual payments of $4210.00 for 8.5 years. If the first payment is due on the date of purchase and interest is 8.53% compounded quarterly, what is the purchase price of the property?

Question 44

Ellora wants to accumulate $150 000.00 in an RRSP by making annual contributions of $5000.00 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

Question 45

Karen Peters bought their neighbor's farm for $450 000.00 down and payments of $67100.00 at the end of every six months for 7 years. What is the purchase price of the farm if the semi-annual payments are deferred for four years and interest is 5.5% compounded semi-annually?

Question 46

Quarterly deposits of $2000.00 were made at the beginning of every 3 months for 10 years. If the interest is 6% compounded monthly, what amount can be withdrawn 7 years after the last deposit?

Question 47

Starting three months after her grandchild Crystal's birth, Mrs. Robinson made deposits of $63.25 into a trust fund every three months until Crystal was 19 years old. The trust fund provides for equal withdrawals at the end of each quarter for 5 years beginning three months after the last deposit. If interest is 8.24% compounded quarterly, how much will Crystal receive every three months?

Question 48

What is the accumulated value after 14 years of monthly deposits of $415.00 earning interest at 5.8% compounded semi-annually if the deposits are made
a)at the end of each month?
b)at the beginning of each month?

Question 49

Determine the accumulated value after 15 years of deposits of $500.00 made at the beginning of every 6 months and earning interest at 12% compounded monthly?

Question 50

Mike acquired his sister's share of their business by agreeing to make payments of $4711.00 at the end of each year for 8 years. If the payments are deferred for three years and money is worth 5.96% compounded quarterly, what is the cash value of the sister's share of the business?

Question 51

A property was purchased for quarterly payments of $1070.00 for 9 years. If the first payment was made on the date of purchase and interest is 5.57% compounded annually, what was the purchase price of the property?

Question 52

A property was purchased for quarterly payments of $3000.00 for 10 years. If the first payment was made on the date of purchase and interest is 6% compounded annually, what was the purchase price of the property?

Question 53

A lease requires monthly payments of $1150.00 due in advance. If interest is 16% compounded quarterly and the term of the lease is 4 years, what is the cash value of the lease?

Question 54

At the beginning of every 6 months, $1280.00 is deposited for 8 years at 6.6% compounded monthly. After 8 years interest for the account is to be 9.66% compounded quarterly and the account is to be paid out by equal end-of-quarter quarterly payments over 6 years. What is the size of the quarterly payment?

Question 55

Determine the accumulated value after 14.5 years of deposits of $172.00 made at the beginning of every 6 months and earning interest at 4.45% compounded monthly?

Question 56

Billy Bean contributes $415.00 at the beginning of each month into RRSP paying interest at 6.25% compounded semi-annually. What will be the accumulated balance in the RRSP at the end of 14.75 years?

Question 57

Quarterly deposits of $650.00 were made at the beginning of every 3 months for 11.25 years. If the interest is 4.92% compounded monthly, what amount can be withdrawn 6 years after the last deposit?

Question 58

A vacation property was bought by making semi-annual payments of $7500.00 for seven years. If the first payment is due on the date of purchase and interest is 6% p.a. compounded quarterly, calculate the purchase price of the property.

Question 59

Slick Sean contributes $500.00 at the beginning of each month into RRSP paying interest at 6.00% compounded semi-annually. What will be the accumulated balance in the RRSP at the end of 15 years?

Question 60

Compute the nominal annual rate of interest compounded monthly at which $1500.00 deposited at the beginning of every three months for ten years will amount to $90 000.00.

Question 61

Oakville Aqua Club bought swimming equipment on a contract requiring monthly payments of $1000 for 5 years beginning 6 months after the date of purchase. What was the cash value of the equipment if interest is 12% compounded monthly?

Question 62

A sum of money is deposited at the end of every 6 months for 9.5 years at 8% compounded semi-annually. After the last deposit, interest for the account is to be 4.5% compounded quarterly and the account is to be paid out by making payments of $4360.00 at the end of each month over 7.75 years. What is the size of the semi-annual deposit?

Question 63

Mark contributed $270.00 at the end of every 3 months for 5.75 years into an RRSP earning 12.6% interest compounded quarterly. Four years after the last contribution he converted the RRSP into a RRIF that is to pay him quarterly payments for 29.5 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 9.5% compounded quarterly, how much will Mark receive every 3 months?

Question 64

Mrs. Martin contributes $1830.00 at the beginning of every three months to an RRSP. Interest on the account is 7.44% compounded quarterly.
a)What will the balance in the account be after 6 years?
b)How much of the balance will be interest?
c)If Mrs. Martin converts the balance after 6 years into an RRIF paying 5.41% compounded quarterly and makes equal quarterly withdrawals for 11 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal?
d)What is the combined interest earned by the RRSP and the RRIF?

Question 65

A debt of $140 000.00 is to be repaid in installments due at the end of each month for 15.5 years. If the payments are deferred for three years and interest is 7.28% compounded quarterly, what is the size of the monthly payments?

Question 66

Mrs. Lavergne deposits $562.71 at the beginning of every three months. Starting three months after the last deposit, she intends to withdraw $587.00 every three months for 16 years. If interest is 8.14% compounded quarterly, for how long must Mrs. Lavergne make deposits?

Question 67

A sum of money is deposited at the end of every month for 9 years at 8.5% compounded monthly. After the last deposit, interest for the account is to be 8.1% compounded quarterly and the account is to be paid out by end-of-quarter quarterly payments of $1800.00 over 7 years. What is the size of the monthly deposit?

Question 68

The amount of $75 400.00 is invested at 9.65% compounded quarterly for 3 years. After 3 years the balance in the fund is converted into an annuity. If interest on the annuity is 6.75% compounded semi-annually and payments are made at the end of every six months for 8 years, what is the size of the payments?

Question 69

TJ invested a retirement gratuity of $43 000.00 in an income averaging annuity paying 7% compounded monthly. He withdraws the money in equal monthly amounts over five years. If the first withdrawal is made nine months after the deposit, what is the size of each withdrawal?

Question 70

Anne-Marie received $445 000.00 from her mother's estate. She wants to set aside part of her inheritance for her retirement 12 years from now. At that time she would like to receive a pension supplement of $2600.00 at the end of each month for 15 years. If the first payment is due one month after her retirement and interest is 3.6% compounded monthly, how much must Anne-Marie set aside?

Question 71

A sum of $15 700.00 is invested at 6.48% compounded semi-annually for eight years. After the eight years, the balance in the fund is converted into an annuity paying equal payments at the end of every 6 months for 5.5 years. If interest on the annuity is 7.95% compounded monthly, what is the size of the equal payments?

Question 72

Equal payments are to be made at the end of each month for 12 years with interest at 9.66% compounded monthly. After the last payment, the fund is to be invested for 4 years at 6.82% compounded quarterly and have a maturity value of $27 600.00. What is the size of the monthly payment?

Question 73

$6420.00 was invested at a fixed rate of 6.5% compounded semi-annually for 5 years. After 5 years, the fund was converted into an ordinary annuity paying $550.00 per month. If interest on the annuity was 6% compounded monthly, what was the term of the annuity?

Question 74

Beverley intends to retire in 7.25 years and would like to receive $2700.00 every month for 12.25 years starting on the date of her retirement. How much must she deposit in an account today if interest is 11.36% compounded annually?

Question 75

The Saskatchewan Junior Achievers need to borrow to finance a project. Repayment of the loan involves payments of $8711.00 at the end of every three months for six years. No payments are to be made during the development period of three years. Interest is 9.24% compounded quarterly.
a)How much did the Achievers borrow?
b)What amount will be repaid?
c)How much of that amount will be interest?

Question 76

Mr. Caldwell received a retirement gratuity of $48 700.00, which he deposited in an RRSP. He intends to leave the money for 6 years, then transfer the balance into an RRIF and make equal withdrawals at the end of every six months for 25 years. If interest is 8.5% compounded semi-annually, what will be the size of each withdrawal?

Question 77

The local high school soccer club need to borrow to finance a new soccer field. Repayment of the loan involves payments of $10 000.00 at the end of every three months for eight years. No payments are to be made during the development period of five years. Interest is 8% compounded quarterly.
a)How much did the Achievers borrow?
b)What amount will be repaid?
c)How much of that amount will be interest?

Question 78

Flin Flon Aqua Club bought swimming equipment on a contract requiring monthly payments of $815.50 for 4 years beginning 11 months after the date of purchase. What was the cash value of the equipment if interest is 7.8% compounded monthly?

Question 79

A man received a separation payment of $98 000.00 at age 56. He invested that sum of money at 8.5% compounded semi-annually until he was 65. At that time he converted the existing balance into an ordinary annuity paying $6150.00 every 6 months, with interest at 5% compounded semi-annually. How many payments will be made?

Question 80

Monica would like to receive $3760.00 at the end of every six months for 8 years after her retirement. If she retires ten years from now and interest is 6.5% compounded semi-annually, how much must she deposit into an account every six months starting now?