Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

National Research Council is considering the establishment in perpetuity of a Visiting Professor chair at UOIT. The ongoing cost will be $12 500 at the end of each month. If the money can earn 8% compounded monthly in perpetuity, what endowment is required to fund the position?

You start to save for a major purchase. You can invest $329 every three months starting today for 5 years and 9 months. You are able to earn 5.87% compounded semi-annually. What is the amount of interest that you earn during the entire term?

Note: The calculations for this question were done using Excel's RATE function. A vacation property valued at $62 000.00 was bought for 40 payments of $2150.00 due at the beginning of every six months. What nominal rate of interest was charged?

National Research Council is considering the establishment of $2 million endowment held in perpetuity of a Visiting Professor chair at UOIT. The ongoing cost will be $12 500 at the end of each month. What monthly compounded nominal rate of return must be earned to fully fund the position?

Jack Chen makes deposits of $415.00 at the beginning of every three months. Interest earned by the deposits is 4.12% compounded quarterly. a) What will the balance in Jack's account be after eight years? b) How much of the balance will Jack have contributed? c) How much of the balance is interest?

Enermax offers to acquire a right-of-way from a property owner who receives annual lease payments of $3725.00 due in advance. What is a fair offer if money is worth 6.5% compounded quarterly?

What sum of money must be deposited in a savings scholarship account to provide a scholarship of $3320.00, payable at the beginning of each 3 months, if interest is 3.59% compounded quarterly?

An annuity provides payments of $4580.00 at the end of every three months. The annuity is bought for $53 500.00 and payments are deferred for 10 years. If interest is 9.72% compounded monthly, for how long will payments be received?

Goggle Inc. is planning to pay a quarterly dividend of $0.50 on its perpetual preferred share. The market requires a dividend yield of 5% compounded annually on preferred shares of similar risks. What is the fair market value of its perpetual preferred share just after payment of a dividend at the end of the quarter?

Mike acquired his sister's share of their business by agreeing to make payments of $4711.00 at the end of each year for 8 years. If the payments are deferred for three years and money is worth 5.96% compounded quarterly, what is the cash value of the sister's share of the business?

Erica intends to retire in 37.5 years and would like to receive $6600.00 every 6 months for 14 years, starting on the date of her retirement. How much must she deposit in an account today if interest is 6.25% compounded semi-annually?

Witzke retired from Ontario Hydro and received a payment of $980 000.00 at age 56. He invested that sum of money at 5.5% compounded semi-annually until he was 65. At that time he converted the existing balance into an ordinary annuity paying $10 250.00 every month, with interest at 5% compounded monthly. How many payments will be made?

OPG has set up a fund to help pay the expenses for the monitoring of Pickering nuclear power plant once it is in safe storage. The balance in the fund today is $700 million, and it will earn interest at 7% compounded annually. Starting 10 years from now, $100 million will be withdrawn from the fund at the beginning of every year for 30 years. What is the annually compounded interest rate for the fund during the final 30 years?

Asif received a bonus of $10 000, which he immediately invested in a fund earning 9.25% compounded semi-annually through his Tax Free Savings Account. Five years later, Asif plans to make the first semi-annual withdrawal of $1000. After how many withdrawals, the fund will be completely depleted?

Tricia bought a living-room suite on credit, signing an installment contract with a finance company that requires monthly payments of $167.25 for 4.5 years. The first payment is made on the date of signing and interest is 28.8% compounded monthly. a) What was the cash price? b) How much will Tricia pay in total? c) How much of what she pays will be interest?

A property was purchased for quarterly payments of $3000.00 for 10 years. If the first payment was made on the date of purchase and interest is 6% compounded annually, what was the purchase price of the property?

What is the accumulated value after 15 years of monthly deposits of $500.00 earning interest at 8% compounded semi-annually if the deposits are made a) at the end of each month? b) at the beginning of each month?

Leons has a promotion on a refrigerator selling for $1750. Buyers will pay "no money down and no payments for six months." The first of 12 equal monthly payments is required 6 months from the purchase date. What should the monthly payments be if Leons is to earn 15% compounded monthly on its account receivable during both the deferred period and repayment period?

A sum of money is deposited at the end of every 6 months for 9.5 years at 8% compounded semi-annually. After the last deposit, interest for the account is to be 4.5% compounded quarterly and the account is to be paid out by making payments of $4360.00 at the end of each month over 7.75 years. What is the size of the semi-annual deposit?

How much does a depositor have to save at the beginning of every three months for 13.25 years to accumulate $41 600.00 if interest is 8% compounded quarterly?