Exam 12: Annuities: Special Situations

Gregory deposits a $30,000 for a period of time at a 3.5% rate of interest compounded semi-annually. The accumulated amount provides Gregory the benefit of withdrawing $1,165 at the end of each month for three years. Determine how long the initial deposit accumulated interest.

What amount can be paid at the end of every month, in perpetuity, from an endowment of $75,000 earning 8% compounded monthly?

A legal dispute delayed for 18 months the disbursement of a $500,000 bequest designated to provide quarterly payments in perpetuity to a hospice. While under the jurisdiction of the court, the funds earned interest at the rate of 5% compounded semi-annually. The hospice has just invested the $500,000 along with its earnings in a perpetual fund earning 5.2% compounded semi-annually. What payments will the hospice receive beginning three months from now?

A perpetuity is to pay $10,000 at the end of every six months. How much less money is required to fund the perpetuity if the money can be invested to earn 5% compounded semi-annually?

An old agreement requires a town to pay $500 per year in perpetuity to the owner of a parcel of land for a water-well dug on the property in the 1920s. The well is no longer used, and the town wants to buy out the contract, which has become an administrative nuisance. What amount (including the regular scheduled payment) should the landowner be willing to accept on the date of the next scheduled payment if long-term low-risk investments now earn 3.8% compounded annually?

Nino plans to initially contribute $10,000 and increase his yearly contributions by 2% each year for 15 years. If the rate of interest is 4% compounded annually, determine how much the investment will be worth in 15 years.

We will make annual RRSP contributions at the end of every year for 35 years and each contribution is going to be 8% larger than the previous one. Our goal is to have $2,000,000 in 35 years. The RRSP will earn 13% compounded annually. How large will the first contribution be?

The common shares of Unicorp. are forecast to pay annual dividends of $2 at the end of each of the next five years, followed by dividends of $3 per year in perpetuity. What is the fair market value of the shares if the market requires a 8% annually compounded rate of return on shares having a similar degree of risk?

Mrs. Lyons has deposited $175,000 at 5.25% compounded quarterly. In 10 years, she plans to convert the accumulated amount into a perpetuity, in which she will receive the same amount at the end of each month. What is the maximum payment she can receive if the interest rate stays the same?

An endowment fund of $5,000,000 is to pay out grants for medical research. The grants are to be paid once per month and the first one is to be paid today. The fund will earn interest at 11% compounded semi-annually. What is the size of the monthly grants?

A wealthy donor made a $50,000 contribution to a local charity. The charity invested this amount for three years at an interest rate of 2.4% compounded annually. At the end of this time, the charity wished to provide monthly benefits in perpetuity to those in need. Determine the amount that the charity can provide on a monthly basis.

Fred intends to retire in 10 years. To supplement his pension, he would like to receive $500 every six months for 20 years. If he is to receive the first payment six months after the date of his retirement, what lump amount must he invest today to achieve his goal? Assume that the investment will earn 12% compounded semi-annually.

What amount is required to fund a perpetuity that pays $10,000 at the beginning of each quarter? The funds can be invested to earn 5% compounded quarterly.

What amount, invested today at 5% compounded quarterly, will support perpetual monthly payments of $800? The first payment will be made one month from now.

What amount can be paid at the end of every six months, in perpetuity, from an endowment of $475,000 earning 7% compounded annually?

How much will it cost to buy a 20-year monthly annuity that grows at 2.5% compounded monthly, if the first payment is $1,500 and money is worth 4.25% compounded monthly?

An individual wants to receive end-of-month payments of $1,200 for 20 years after she retires 15 years from now. What lump amount must she invest today to provide the retirement income? Assume the investment earns 7% compounded monthly for the entire 35 years.

Calculate the present value of a perpetuity that will pay out $7,500 every six months. The first payment will be made four years from now. The interest rate earned is 8.6% compounded semi-annually.

A $35,000 loan bearing interest at 10% compounded quarterly was repaid, after a period of deferral, by quarterly payments of $1573.83 over 12 years. What was the time interval between the date of the loan and the first payment?

To sell a farm that it had acquired in a foreclosure action, the Royal Bank agreed to monthly payments of $2,700 for 20 years, with the first payment due 15 months from the date of sale. If the purchaser paid 15% down and the interest rate on the balance is 9% compounded annually, what was the purchase price?