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Exam 12: Annuities: Special Situations

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Question 21

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What amount must be placed in a perpetual fund today if the fund earns 4.25% compounded semi-annually, and payments of $2500 are to be made monthly, starting two years from today?

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Question 22

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

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Question 23

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$30,000 is placed in a fund earning 7% compounded quarterly. How many quarterly withdrawals of $2,000 can be made if the first withdrawal occurs three years from today? Count the final withdrawal, which will be less than $2,000.

What is the fair market value of a perpetual preferred share just after the semi-annual dividend of $.60 has been paid if shares of similar risk are earning 7.25% compounded semi-annually?

Mr. Parmar wants to retire in 20 years and purchase a 25-year annuity that will make equal payments at the end of every quarter. The first payment should have the purchasing power of $6,000 in today's dollars. If he already has $54,000 in his RRSP, what contributions must he make at the end of every half-year for the next 20 years to achieve his retirement goal? Assume that the rate of inflation for the next 20 years will be 2.5%, the RRSP will earn 8% compounded semi-annually, and the rate of return on the fund from which the annuity is paid will be 5.5% compounded quarterly.

How much money would accumulate over 35 years if the investor makes an investment of $3,500 at the end of the first year and always increases the size of the annual investment by 5% over the previous year. The investments are expected to earn 11% compounded annually.

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 amount of money invested now will provide payments of $500 at the end of every month for five years following a four-year period of deferral? The money will earn 5.4% compounded monthly.

The National Museum has received a donation of $2,000,000 which is to be used to purchase new exhibits at the end of every three months. If the money earns 12% compounded annually, how much could be paid out every three months in perpetuity?

If a donation of $100,000 is expected to pay out scholarships of $10,000 every year and the funds earn 7.5% compounded annually, how long will it be before the first annual payment can be made?

A property development company obtained a $2.5 million loan to construct a commercial building. The interest rate on the loan is 5% compounded semi-annually. The lender granted a period of deferral until rental revenues become established. The first quarterly payment of $100,000 is required 21 months after the date of the loan. How long after the date of the original loan will the last payment be made?

A city sells plots in its cemetery for $1,000 plus an amount calculated to provide for the cost of maintaining the grounds in perpetuity. This cost is figured at $25 per plot due at the end of each quarter. If the city can invest the funds to earn 4.8% compounded annually in perpetuity, what is the price of a plot?

Dean has already implemented the first stage of his financial plan. Over a 30-year period, he will continue to increase his annual year-end RRSP contributions by 2% per year. His initial contribution was $2,000. At the end of the 30 years, he will transfer the funds to an RRIF and begin end-of-month withdrawals that will increase at the rate of 1.8% compounded monthly for 25 years. Assume that his RRSP will earn 6% compounded annually and his RRIF will earn 3% compounded monthly. What will be the size of his initial RRIF withdrawal?

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

Mr. Haddit plans to retire eight years from today. He projects that he will need $30,000 per year in his retirement which he assumes will be for 15 years. The first payment will be nine years from today. To fund his retirement, Mr. Haddit will invest a lump amount today and later use it to sustain the 15 withdrawals. If his investment earns 6% compounded annually, how much must he invest today?

Negotiations between Delco Manufacturing and the union representing its employees are at an impasse. The union is seeking a 4.5% wage increase. Delco's offer is 2%. The employees have passed a vote authorizing job action. Suppose the union succeeds in winning the 4.5% increase after a two-month strike. For an employee 10 years from retirement, will there be any economic gain? Compare the current economic values of (1) 10 years' end-of-month wages at the employer's offer (102% of last year's wages) vs. (2) wages including a 4.5% increase to the same horizon but after a two-month strike. Assume money is worth 6% compounded monthly.

What is the amount of the initial deposit required to have an RRSP account of $750,000 in 40 years, if deposits are made at the end of each quarter, the plan allows for a 2.5% adjustment for inflation, and money earns 3.8% compounded quarterly?

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

Nancy borrowed $8,000 from her grandfather to buy a car when she started college. The interest rate being charged is only 4.5% compounded monthly. Nancy is to make the first $200 monthly payment on the loan three years after the date of the loan. How long after the date of the initial loan will she make the final payment?

Determine the periodic payment for the following deferred annuity. The annuity is an ordinary annuity following the period of deferral.