Exam 12: Annuities: Special Situations

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.

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

Mr. O'Connor set up a trust account paying $500 per month in perpetuity to the local hospital. These payments consume all the interest earned monthly by the trust. Between what amounts does the balance in the trust account fluctuate if it earns 6% compounded monthly?

A wealthy benefactor has donated $1,000,000 to establish a perpetuity that is to pay a constant payment once per month. The money will earn 10% compounded annually. The first monthly perpetual payment will be made 28 months from now. Determine the size of the payments.

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

Mrs. Clare left $150,000 to her local college for an annual scholarship for students in need. What is the amount of the scholarship if the fund earns 3.75% compounded annually?

What is the fair market value of a perpetual preferred share just after the quarterly dividend of $1.40 has been paid if shares of similar risk are earning 5.5% compounded annually?

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

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

If money can earn 6% compounded annually, what percentage more money is required to fund an ordinary perpetuity paying $1,000 at the end of every year than to fund an ordinary annuity paying $1,000 per year for 25 years?

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?

Mrs. Clare wants to set up a college fund for her daughter so that she will have a monthly income of $500 each month for three years starting 10 years from now. How much should she deposit today if money earns 4.25% compounded monthly?

During a one-week promotion, Al's Appliance Warehouse is planning to offer terms of "nothing down and nothing to pay for four months" on major appliances priced above $500. Four months after the date of sale, the first of eight equal monthly payments is due. If the customer is to pay interest at the rate of 12% compounded monthly on the outstanding balance from the date of sale, what will be the monthly payments on an automatic dishwasher priced at $995?

Mrs. McTavish wants to establish an annual $5,000 scholarship in memory of her husband. The first scholarship is to be awarded two years from now. If the funds can earn 6.25% compounded annually, what amount must Mrs. McTavish pay now to sustain the scholarship in perpetuity?

An investment of $50 is to be made at the end of this month and that amount is increased by 1% every month for 40 years. The investments are expected to earn 13.2% compounded monthly. What should be the total value of these investments in 40 years?

You wish to donate $10,000 to a local charity in order for it to provide annual benefits of $750 per year in perpetuity. If interest is compounded monthly, determine the interest rate needed to fulfil this goal.

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?

The common shares of Bancorp Ltd. are forecast to pay annual dividends of $3 at the end of each of the next five years, followed by dividends of $2 per year in perpetuity. What is the fair market value of the shares if the market requires a 5% annually compounded rate of return on shares having a similar degree of risk?

Hard Rock Paving Company is applying for a loan. It is your job to determine how much they will be able to borrow. They will not be making any payments for the first 15 months. After that, they will make payments of $1,000 per month for four years. There is no interest-free grace period. The first $1,000 payment will be made 15 months after the loan is received. If the interest rate is 13.2% compounded monthly, how much can they expect to borrow?

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