Exam 12: Annuities: Special Situations

A donation of $250,000 is made today to the local library for the purchase of new books. What amount can be withdrawn every month in perpetuity if the money is earning 9% compounded monthly and the first payment is to be made immediately?

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?

Mrs. O'Halloran gave $130,000 to the University of Northern British Columbia for a perpetual scholarship fund. What amount can be awarded on each anniversary if the scholarship fund earns 7% compounded annually?

Fred asked two life insurance companies to give quotes on a 20-year deferred annuity (after a 5-year deferral period) that can be purchased for $100,000. Northwest Mutual quoted payments of $875 payable at the end of each month. Liberty Standard stated that all their annuity options provide a rate of return equal to 5.5% compounded annually. Which should Fred choose?

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?

A business group is considering establishing an endowment to allow eligible employees an opportunity to further their education. The amount of the grant available will be $10,000 per month. If the amount the business group is investing is $2 million, what nominal rate of return must the investment earn to fully fund the grant?

What is the current economic value of an inheritance that will pay $2,500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5¼ years from now? Assume that money can earn 6% compounded monthly.

How much will it cost to purchase a 20-year indexed annuity in which the end-of-quarter payments start at $5,000 and grow by 2% compounded quarterly? Assume that the money used to purchase the annuity earns 6% compounded quarterly.

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

What amount must be invested today to allow for quarterly payments of $2,500 at the end of every quarter for 15 years after a six-year deferral period? Assume that the funds will earn 5% compounded semi-annually.

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 current economic value of an inheritance that will pay $2,500 to the beneficiary at the beginning of every three months for 20 years starting when the beneficiary reaches 21 years of age, 5¼ years from now? Assume that money can earn 6% compounded monthly.

What price will a finance company pay to a merchant for a conditional sale contract that requires 15 monthly payments of $231 beginning in six months? The finance company requires a rate of return of 18% compounded monthly.

Marion's grandfather will establish a trust that will pay her $1,500 every three months for 11 years. The first payment will be made six years from now, when she turns 19. If money is worth 6.5% compounded quarterly, what is today's economic value of the bequest?

Leslie received a $40,000 settlement when her employer declared her job redundant. Under special provisions of the Income Tax Act, she was eligible to place $22,000 of the amount in an RRSP. Fifteen years from now, she intends to transfer the money from the RRSP to a Registered Retirement Income Fund (RRIF). Thereafter, Leslie will make equal withdrawals at the end of each quarter for 20 years. If both the RRSP and the RRIF earn 8.5% compounded quarterly, what will be the amount of each withdrawal?

Evergreen Landscaping is applying for a loan. Your help is needed to determine how much they can borrow. They will not be able to make any payments for the first 18 months. After that, they will make payments of $750 per month for five years. There is no interest-free grace period. The first $750 payment will be made 18 months after the loan is received. If the interest rate is 10.5% compounded monthly, how much can they expect to borrow?

We are aiming to have $5,000,000 in 45 years and we plan to get there by making monthly investments that are 1% larger than the previous month's investment. Our funds will earn 14.4% compounded monthly. How much should be invested at the end of the first month?

Calculate the present value of a deferred annuity of 20 annual payments of $100,000 each The interest rate is 13.5% compounded annually and the first payment will be made 11 years from now.

$10,000 was invested in a fund earning 7.5% compounded monthly. How many monthly withdrawals of $300 can be made if the first occurs 3½ years after the date of the initial investment? Count the final smaller withdrawal.

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