Exam 12: Annuities: Special Situations

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?

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

What is the present value of a trust fund that earns 8.8% compounded annually and pays out $3,500 every three months? The next payment is due to be made today.

Anita is planning to go back to school in 2 years. Once at school, she wishes to be able to withdraw $900 at the end of each month for 2 years. If interest is 4.5% compounded monthly, determine the amount that should be deposited now to fulfil her goal.

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.

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

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.

Suppose year-end contributions to an RRSP start at $3,000 and increase by 2.5% per year thereafter. What will be the amount in the RRSP after 25 years if the plan earns 9% compounded annually?

Marion wants to buy an investment that will pay her $2,000 for the first month, and include a 3% growth rate compounded monthly for each subsequent monthly payment. The term of the investment is for 25 years, and Marion wants to start receiving the payments 10 years from now. What amount should she deposit today to reach her goal if the investment can earn 6% compounded monthly?

What amount invested today will provide yearly payments of $50,000 for 20 years starting 10 years from now if invested at 5.5% compounded annually?

Mr. Chan has donated $1 million to a college to set up a perpetuity for the purchase of books and journals for a new library to be built and named in his honour. The donation will be invested and earnings will compound for three years, at which time the first of the quarterly perpetuity payments will be made. If the funds earn 6% compounded quarterly, what will be the size of the payments?

Simon Fraser recently received a $20 million donation to be used for scholarship purposes. If interest can be earned at 4.2% compounded monthly, determine the semi-annual amount of scholarships that students can apply for.

Mrs. Corriveau has just retired at age 58 with $299,317 in her RRSP. She plans to live off other savings for a few years and allow her RRSP to continue to grow on a tax-deferred basis until there is a sufficient amount to purchase a 25-year annuity paying $2,000 at the end of each month. If her RRSP and the annuity each earn 3.75% compounded monthly, how much longer must she let her RRSP grow (before she buys the annuity)?

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

A $20,000 investment will be allowed to grow at 4.5% compounded semi-annually until it can support semi-annual withdrawals of $1,000 for 20 years. Rounded to the nearest month, how long before the first withdrawal must the investment be allowed to grow?

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

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

What amount, invested today at 6% compounded monthly, will support perpetual monthly payments of $500? The first payment will be made one month from now.

Harold is planning to retire in 21 years. After that he will need an income of $4,500 at the end of every month for the subsequent 25 years. He is going to make one investment today to provide all of the money he will eventually collect. His investments will earn 9% compounded monthly. How much should he invest today?

Moses' goal, when he retires from work in seven years, is to have $400,000 in his Retirement Fund. Assuming he achieves his goal and the fund earns 7% compounded semi-annually after he retires, what is the amount that Moses will be able to take out of his Retirement Fund at the end of every six months for 25 years after he retires?