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Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

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Question 31

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After retirement, Andy plans to buy bonds in a perpetual fund. What amount must Andy place in a perpetual fund today, if it earns 4.8% compounded semi-annually and the first monthly payment of $500 in perpetuity will be made one year from today?

A) $126 244
B) $120 873
C) $120 396
D) $119 629
E) $125 000

F) All of the above
G) A) and C)

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Question 32

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Abe deposited a sum of money at the end of every month for 15 years at 8.5% compounded monthly. After the last deposit, interest for the account is to be 3.5% compounded quarterly and the account is to be paid out by end-of-quarter quarterly payments of $5905.00 over 17 years. What is the size of the monthly deposit?

A) $560 735
B) $1550
C) $756
D) $1160
E) $1466

F) A) and B)
G) B) and D)

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Question 33

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A fund to provide an annual scholarship of $5700.00 is to be set up. If the first payment is due in three years and interest is 6.4% compounded quarterly, what sum of money must be deposited in the scholarship fund today?

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?

You make six monthly deposits of $125 starting now. The interest rate is 6.36% compounded monthly. How much interest has been earned in total?

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 If the interest is 6% compounded monthly, what amount can be withdrawn 7 years after the last deposit?

Sue won a "Millionaire Life" lottery. As a winner of the Grand Prize, she can choose either $1 million per year for 25 years or a single cash payment of $17 million. What option should be chosen if the payments are made at the beginning of each year and on low risk investments, money can earn 3.2% compounded annually?

Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the start of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded monthly.

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?

Keith bought a lakeside cottage for 30% down and monthly mortgage payments of $1224.51 at the beginning of each month for 20 years. Interest is 4.4% compounded semi-annually. What is the purchase price of the property?

Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded monthly. If he puts the money in his savings account at the beginning of each month, what will be the balance in the account at the end of the three-year term?

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?

Jamal plans to retire in 17 years. He is saving $2000 every start of the month in a retirement savings account paying him a long-term interest of 9% compounded monthly until retirement. The rate changes following the retirement. He wants $7000 per month paid to him at the start of the month for 20 years after the retirement. At what rate should his savings account pay him to fulfill his dream? (Use the Rate function in Excel)

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?

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?

Joshua deposited $3560.00 at the beginning of every 6 months for 11 years into a fund paying 3.5% compounded semi-annually. Fourteen years after the first deposit he converted the then existing balance into an annuity due paying him equal annual payments for 22 years. If interest for the annuity due is 5% compounded annually, what is the size of the annual payment?

Rousan contributed $1900.00 at the beginning of every month to an RRSP. Interest on the account is 4.95% compounded monthly. If she converted the balance after 13 years into an RRIF paying 7.1% compounded quarterly and makes equal quarterly withdrawals for 20 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal?

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?

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?

What sum of money must be deposited in a trust fund to provide a scholarship of $1520.00, payable at the beginning of each 3 months, if interest is 6.72% compounded quarterly?