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Exam 12: Annuities: Special Situations

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Question 41

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Mary needs a pension that will pay her $12,000 one year from now and annual payments for 24 more years that are each 5% larger than the previous year. If the funds in her Retirement Fund earn 7.5% compounded annually, how much money must she have there now?

A) $188,490
B) $266,540
C) $532,842
D) $213,460
E) $487,671

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Question 42

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Fred asked two life insurance companies to give quotes on a 20-year deferred annuity (after a 5-year deferral period) that can be purchased for $100,000. Northwest Mutual quoted payments of $875 payable at the end of each month. Liberty Standard stated that all their annuity options provide a rate of return equal to 5.5% compounded annually. Which should Fred choose?

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Question 43

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The Willie P. Stanton Trust Fund is to pay, $5,000 at the end of every year to the student-athlete voted most deserving based on his or her dedication to the ideals of good citizenship. The Trust Fund earns 7.4% compounded semi-annually. What is the present value of this perpetuity?

Maritime Bank recently announced that its next semi-annual dividend (to be paid six months from now) will be $1.00 per share. A stock analyst's best estimate for the growth in future dividends is 4% compounded semi-annually. a) If you require a rate of return of 7.8% compounded semi-annually on the stock, what maximum price should you be willing to pay per share? Ignore the present value of dividends beyond a 50-year time horizon. b) What price do you obtain if you do not ignore dividends beyond 50 years? (Hint: Use a large value, say 1000, for n in the present value calculation.)

Harry deposits $10,000 into an investment account that earns 7% compounded monthly. How many monthly withdrawals of $310 will he be able to make if his first withdrawal is exactly five years after his deposit?

Erica is making contributions to her RRSP by depositing an initial $1,500 at the end of December this year, and then increasing the deposit by 8% each year after. What will be the amount of her deposit in the twentieth year?

Harold, just turned 27, wants to accumulate an amount in his RRSP at age 60 that will have the purchasing power of $300,000 in current dollars. What annual contributions on his 28^th through 60^th birthdays are required to meet this goal if the RRSP earns 8.5% compounded annually and the rate of inflation is 2.5% per year?

Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

What is the future value eight years from now of each of the following cash-flow streams if money can earn 9% compounded semi-annually? a) A single payment of $5,000 today. b) An ordinary annuity starting today with eight annual payments of $900. c) An ordinary annuity starting in three years with 20 quarterly payments of $400.

What price will a finance company pay to a merchant for a conditional sale contract that requires 12 monthly payments of $249, with the first payment due six months from now? The finance company requires a return of 16.5% compounded monthly.

Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, what is the amount that Moses will be able to take out of his Retirement Fund at the end of every six months for 25 years after he retires?

Mr. Donatelli moved from Toronto to Winnipeg to take a job promotion. After selling their Toronto home and buying a home in Winnipeg, the Donatellis have $85,000 in cash on hand. If the funds are used to purchase a deferred annuity from a life insurance company providing a rate of return of 8.25% compounded annually, what payments will they receive at the end of every six months for 20 years after a 9-year deferral period?

Mr. Chan has donated $1 million to a college to set up a perpetuity for the purchase of books and journals for a new library to be built and named in his honour. The donation will be invested and earnings will compound for three years, at which time the first of the quarterly perpetuity payments will be made. If the funds earn 6% compounded quarterly, what will be the size of the payments?

Determine the term, expressed in years and months, for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.

A firm obtained a $3 million low-interest loan from a government agency to build a factory in an economically depressed region. The loan is to be repaid in semi-annual payments over 15 years, and the first payment is due three years from today, when the firm's operations are expected to be well established. a) What will the payments be if the interest rate on the loan is 6% compounded semi-annually? b) What is the nominal amount of interest that will be paid over the lifetime of the loan?

In this LO, does constant growth mean that each successive payment increases by the same dollar amount? If not, what does it mean?

Mrs. O'Reilly donated $500,000 to Medicine Hat College for a perpetual scholarship fund for women in business studies. What amount can be awarded on each anniversary if the scholarship fund earns 4½% compounded annually?

A $20,000 investment will be allowed to grow at 4.5% compounded semi-annually until it can support semi-annual withdrawals of $1,000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

Determine the unknown value for the following deferred annuity. The annuity is understood to be an ordinary annuity after the period of deferral.

Mrs. Kirkpatrick (age 65) is about to begin receiving a CPP retirement pension of $9,000 per year. This pension is indexed to the Consumer Price Index (CPI). Assume that the annual pension will be paid in a single year-end payment, the CPI will rise 3% per year, and money is worth 6% compounded annually. What is the current economic value of: a) 20 years of pension benefits? b) 25 years of pension benefits?