Question 1

Fraser deposits $790.00 at the beginning of every three months.He wants to build up his account so that he can withdraw $1550.00 every three months starting three months after the last deposit.If he wants to make the withdrawals for 16 years and interest is 6.64% compounded quarterly,for how long must Fraser make the quarterly deposits?

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Question 2

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?

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Question 3

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?

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Question 4

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made at the beginning of every 3 months for 11.25 years.If the interest is 4.92% compounded monthly,what amount can be withdrawn 6 years after the last deposit?

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Question 5

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.

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Question 6

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?

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Question 7

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?

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Question 8

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?

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Question 9

Jeff is retired and has an investment fund worth $210 000 in an RRSP,which earns 9% compounded semi-annually.He plans to withdraw only $2000 at the beginning of each month starting today.When will the fund become depleted?

Accepted Answer

A) 16 years and 6 months 
B) 16 years 10 months 
C) 8 years and 9 months 
D) 9 years 
E) 17 years

Question 10

What is the principal invested at 8% compounded semi-annually from which monthly withdrawals of $1000.00 can be made at the beginning of each month for 10 years but deferred for 3 years?

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Question 11

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?

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Question 12

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?

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Question 13

Jawad makes semi-annual contributions of $2000 starting on his 27th birthday.How much will he accumulate in his RRSP by age 60,if RRSP earns 8% compounded semi-annually and no contribution is made on his sixtieth birthday?

Accepted Answer

A) $615 535 
B) $640 156 
C) $565 324 
D) $587 937 
E) $669 842

Question 14

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.

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Question 15

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?

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Question 16

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.

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Question 17

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.

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Question 18

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?

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Question 19

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?

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Question 20

National Research Council is considering the establishment in perpetuity of a Visiting Professor chair at UOIT.The ongoing cost will be $12 500 at the end of each month.If the money can earn 8% compounded monthly in perpetuity,what endowment is required to fund the position?

Accepted Answer

A) $156 250 
B) $312 500 
C) $937 500 
D) $1 875 000 
E) $2 000 000

Exam 13: Annuities Due, deferred Annuities, and Perpetuities