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Exam 12: Annuities: Special Situations

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Question 1

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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.

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Question 2

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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 3

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Christian plans to initially contribute $3,000 and increase his yearly contributions by 5% each year for 20 years. If the rate of interest is 7% compounded annually, determine the amount of his payment in year 12.

Calculate the present value of a perpetuity that will pay out $1,500 every month and the first payment is to be made 10 years from now. The interest rate earned is 9% compounded annually.

A $35,000 loan bearing interest at 10% compounded quarterly was repaid, after a period of deferral, by quarterly payments of $1573.83 over 12 years. What was the time interval between the date of the loan and the first payment?

What is the present value of a trust fund that earns 9% compounded monthly and pays out $950 every month? The next payment will be made today.

Mr. Larsen's will directed that $200,000 be invested to establish a perpetuity making payments at the end of each month to his wife for as long as she lives and subsequently to the Canadian Heart Foundation. What will the payments be if the funds can be invested to earn 5.4% compounded monthly?

A company's preferred shares pay a $2 dividend every six months in perpetuity. What is the fair market value of the shares just after payment of a dividend if the dividend yield required by the market on shares of similar risk is a) 4% compounded semi-annually? b) 5% compounded semi-annually?

A retiree of the local college has asked that any money collected for a retirement gift be used to set up a perpetuity scholarship fund for a third-year student in the School of Business. A total of $3750 was collected. If interest earns 4% compounded annually, what will be the amount of the yearly scholarship?

A purchase agreement for a $22,000 truck requires 60 equal payments every six months. If the first payment is due one year after the date of purchase and interest is charged at 18% compounded monthly, what is the size of each payment?

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

Nino plans to initially contribute $10,000 and increase his yearly contributions by 2% each year for 15 years. If the rate of interest is 4% compounded annually, determine how much the investment will be worth in 15 years.

If an endowment fund of $2,327,000 is to be used to pay out grants of $175,000 at the end of every year in perpetuity what effective rate of interest must the funds earn?

Calculate the present value of a 25-year annuity making semi-annual payments that grow at a rate of 4% compounded annually. The first payment is $25,000 and the funds earn 8% compounded semi-annually.

How would you handle cases where successive annuity payments decrease by the same percentage every payment interval?

The fair market value of a preferred share is $45. The share pays a quarterly payment of $.65. An investor is able to purchase the share for $42. What will be the investor's annually compounded rate of return?

A company's preferred shares pay a $1.25 dividend every three months in perpetuity. What is the fair market value of the shares just after payment of a dividend if the rate of return required by the market on shares of similar risk is: a) 5% compounded quarterly? b) 6% compounded quarterly?

Gregory deposits a $30,000 for a period of time at a 3.5% rate of interest compounded semi-annually. The accumulated amount provides Gregory the benefit of withdrawing $1,165 at the end of each month for three years. Determine how long the initial deposit accumulated interest.

Sam wants to set up scholarships for his former secondary school graduating class. He has invested $100,000 into an account that pays 4.5% compounded quarterly. If the scholarships are $1,500 each and presented annually at graduation, how many scholarships can be awarded each year?

Baba Lou plans to retire in 20 years. At that point he plans to collect payments at the end of every six months that are 2% larger than the previous payment and this is to continue for 30 years. The first payment will be $16,500. His retirement plan is expected to earn 7% compounded semi-annually after he retires and 10% compounded annually before he retires. What single investment should he make now to fund the whole retirement plan?