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Exam 12: Annuities: Special Situations

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Question 61

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An investment of $100,000 at 4.75% compounded semi-annually was made so that in 20 years, it can be converted into a perpetuity, which will pay the same amount at the end of each month. What is the maximum payment the investment can pay?

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Question 62

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A $30,000 loan bearing interest at 9% compounded monthly was repaid, after a period of deferral, by monthly payments of $425.10 for 10 years. What was the time interval between the date of the loan and the first payment?

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Question 63

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A wealthy benefactor has donated $1,000,000 to establish a perpetuity that will be used to support the operating costs of a local heritage museum scheduled to open in 3 years' time. If the funds earn 4.8% compounded monthly, what monthly payments, the first occurring three years from now, can the museum expect?

An old agreement requires a town to pay $500 per year in perpetuity to the owner of a parcel of land for a water-well dug on the property in the 1920s. The well is no longer used, and the town wants to buy out the contract, which has become an administrative nuisance. What amount (including the regular scheduled payment) should the landowner be willing to accept on the date of the next scheduled payment if long-term low-risk investments now earn 3.8% compounded annually?

The dividends on the common shares of Mosco Inc. are forecast to grow at 10% per year for the next five years. Thereafter, the best guess is that the annual dividend will grow at the same 3% annual rate as the nominal GNP. A $2.00 dividend for the past year was recently paid. Assume that the required rate of return is 9% compounded annually. What is the fair market value of the shares if we ignore all dividends beyond a 30-year time horizon?

Duncan retired recently and plans to utilize other savings for a few years while his RRSP continues to grow on a tax-deferred basis. The RRSP is currently worth $142,470. How long will it be until the amount in the RRSP is large enough to purchase a 25-year annuity paying $1700 at the end of each month? Assume that the RRSP and the annuity will earn 8.75% compounded semi-annually.

How long is the period deferral if the first quarterly payment of a deferred annuity will be paid 3½ years from today?

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?

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

What is the current economic value of an inheritance that will pay $2,500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5¼ years from now? Assume that money can earn 6% compounded monthly.

Mrs. O'Halloran gave $130,000 to the University of Northern British Columbia for a perpetual scholarship fund. What amount can be awarded on each anniversary if the scholarship fund earns 7% compounded annually?

A business group is considering establishing an endowment to allow eligible employees an opportunity to further their education. The amount of the grant available will be $10,000 per month. If the amount the business group is investing is $2 million, what nominal rate of return must the investment earn to fully fund the grant?

Fred purchased a farm with a down payment of $8,500 and 48 semi-annual payments of $3,000. The first of these payments is to be made two years after the date of purchase. What was the purchase price of the farm if the interest rate charged on the balance is 14% compounded semi-annually?

Evergreen Landscaping is applying for a loan. Your help is needed to determine how much they can borrow. They will not be able to make any payments for the first 18 months. After that, they will make payments of $750 per month for five years. There is no interest-free grace period. The first $750 payment will be made 18 months after the loan is received. If the interest rate is 10.5% compounded monthly, how much can they expect to borrow?

Mrs. Henry wants to receive payments of $1,000 per month for 20 years when she retires in 15 years. She wants to know how much she should deposit into an account today to reach her goal if money is worth 5.75% compounded quarterly?

A $450,000 trust fund earns 8% compounded semi-annually. It is to make perpetual payments at the end of every month. What will be the size of the monthly payments?

Leslie received a $40,000 settlement when her employer declared her job redundant. Under special provisions of the Income Tax Act, she was eligible to place $22,000 of the amount in an RRSP. Fifteen years from now, she intends to transfer the money from the RRSP to a Registered Retirement Income Fund (RRIF). Thereafter, Leslie will make equal withdrawals at the end of each quarter for 20 years. If both the RRSP and the RRIF earn 8.5% compounded quarterly, what will be the amount of each withdrawal?

What amount today will provide payments of $1,500 at the end of each month starting in 10 years, if the principal amount is to remain untouched, and money can earn 4.85% compounded quarterly?

A perpetuity is to pay $10,000 at the end of every six months. How much less money is required to fund the perpetuity if the money can be invested to earn 5% compounded semi-annually?

Fred intends to retire in 10 years. To supplement his pension he would like to receive $500 every six months for 20 years. If he is to receive the first payment six months after the date of his retirement, what lump amount must he invest today to achieve his goal? Assume that the investment will earn 12% compounded semi-annually.