Exam 12: Annuities: Special Situations

What amount of money invested now will provide monthly payments of $200 for five years, if the ordinary annuity is deferred for 3½ years and the money earns 3.75% compounded monthly?

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?

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?

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

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

Calculate the present value of a deferred annuity of 20 annual payments of $25,000 each The interest rate is 8.5% compounded annually and the first payment will be made in six years.

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.

What amount must be placed in a perpetual fund today if the fund earns 3.75% compounded quarterly, and payments of $1,000 are to be made monthly, starting one month from today?

A conditional sale contract requires the debtor to make six quarterly payments of $569, with the first payment due in six months. What amount will a finance company pay to purchase the contract on the date of sale if the finance company requires a rate of return of 16% compounded quarterly?

How much will it cost to buy a 30-year quarterly annuity that grows at 2% compounded quarterly, if the first payment is $3,000 and money is worth 4% compounded quarterly?

A loan of $126,500,000 is to be repaid by annual payments for 25 years. The payments will form a constant growth annuity with each payment being 20% larger than the previous one. The interest rate charged on the loan is 11% compounded annually. What is the size of the first payment?

Ida Ho is about to retire from a government job with a pension that is indexed to the Consumer Price Index (CPI). She is 60 years old and has a life expectancy of 25 years. Estimate the current economic value of her pension which will start at $20,000 per year? For the purpose of this estimation, assume that Ida will draw the pension for 25 years, the annual pension will be paid in a single year-end payment, the CPI will rise 2.5% per year, and money is worth 5% compounded annually. How much of the current economic value comes from indexing?

Edward wishes to have $450,000 in his retirement plans in 25 years. He plans to make annual contributions that will increase by 1% each year. If interest is earned at 5% compounded annually, determine the value of the initial payment in year 1.

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

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?

An 18-year-old college student plans to save a "Buck-A-Day" in a glass jar and after one year, set up a Retirement Savings Plan with $365. One year later he will make his second contribution to the RSP but it will be 10% larger than the first one. He will continue to increase his annual contributions by 10%. He anticipates that his investments can earn an annual return of 12.5% compounded annually. How much money is he expecting to have in the RSP after 40 years?

How long (before the first withdrawal) must a $19,665 investment earning 9.5% compounded semi-annually be allowed to grow before it can provide 60 quarterly withdrawals of $1,000?

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?

Mrs. Hunking wants to set up a fund so that she will receive $2500 at the end of each quarter starting in 20 years, but leave the principal amount untouched. If interest is 4.25% compounded semi-annually, how much would she have to deposit today to reach her goal?

As of Brice's 54^th birthday, he has accumulated $154,000 in his Registered Retirement Savings Plan (RRSP). What size of end-of-month payments in a 20-year annuity will these funds purchase at age 65 if he makes no further contributions? Assume that his RRSP and the investment in the annuity will earn 8.25% compounded monthly.