Exam 12: Annuities: Special Situations

Ken Tuckie is about to buy a 25-year annuity that will deliver end-of-month payments. The first payment will be $1,000. How much more will it cost to index the annuity so that payments grow at the rate of 2.4% compounded monthly? Assume the money used to purchase the annuity earns 5.4% compounded monthly.

What price will a finance company pay to a merchant for a conditional sale contract that requires 12 monthly payments of $249, with the first payment due six months from now? The finance company requires a return of 16.5% compounded monthly.

How much more money is required to fund an ordinary perpetuity than a 30-year ordinary annuity if both pay $5,000 quarterly and money can earn 5% compounded quarterly?

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

Heather is planning to retire in 10 years. She will then need an income of $1,500 at the end of every month for the subsequent 25 years. She is going to make one investment today to provide all of the money she will eventually collect. Her investments will earn 12% compounded monthly. How much should she invest today?

The Pithybottoms want to make a donation to set up a scholarship trust fund at Hinose College. The fund is to support payments of $5,000 at the end of every three months in perpetuity. If the fund earns 7.5% compounded quarterly, how much must they donate?

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

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?

What is the amount of the initial deposit required to have an RRSP account of $1 million in 30 years, if deposits are made at the end of each month, the plan allows for a 2% adjustment for inflation, and money earns 4% compounded monthly?

Andy deposits $40,000 into an account earning 6.6% compounded annually for 5 years. After this time, Andy wishes to withdraw $2,814.41 at the end of each quarter and have $10,000 remaining. Determine the number of withdrawals Andy can make.

A local college provides annual scholarships totalling $5,000 to business students. If interest is at 3.1% compounded quarterly, determine the original amount that was deposited.

What semi-annual compounded nominal rate of return is required to return $5,000 every six months if the perpetuity fund is $265,000?

Mrs. O'Reilly donated $500,000 to Medicine Hat College for a perpetual scholarship fund for women in business studies. What amount can be awarded on each anniversary if the scholarship fund earns 4½% compounded annually?

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?

Erica is making contributions to her RRSP by depositing an initial $1,500 at the end of December this year, and then increasing the deposit by 8% each year after. What will be the amount of her deposit in the twentieth year?

What quarterly compounded nominal rate of return is required to return $2,000 per quarter if the perpetuity fund is $98,000? What is the effective rate of interest?

Ranger Oil recently donated $750,000 to the Northern Alberta Institute of Technology (NAIT) to fund (in perpetuity) five annual bursaries for students in Petroleum Engineering Technology. If the first five bursaries are to be awarded immediately, what is the maximum amount of each bursary? Assume that the bursary fund earns 4.9% compounded semi-annually.

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

How much more money is required to fund an ordinary perpetuity than a 25-year ordinary annuity if the funds can earn 7% compounded quarterly and both pay $500 monthly?

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