Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Keith bought a lakeside cottage for 30% down and monthly mortgage payments of $1224.51 at the beginning of each month for 20 years. Interest is 4.4% compounded monthly. What is the purchase price of the property?

Mark contributed $270.00 at the end of every 3 months for 5.75 years into an RRSP earning 12.6% interest compounded quarterly. Four years after the last contribution he converted the RRSP into a RRIF that is to pay him quarterly payments for 29.5 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 9.5% compounded quarterly, how much will Mark receive every 3 months?

Robert Downey deposited $610.00 in a trust account on the day of his son's birth and every three months thereafter. If interest paid is 7.2% compounded quarterly, what will the balance in the trust account be before the deposit is made on the son's twenty-first birthday?

Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually. Seven years after the last contribution, Amy converted the RRSP into an RRIF that is to pay her equal quarterly amounts for 17.25 years. If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 7.66% compounded quarterly, how much will Amy receive every three months?

A lease requires monthly payments of $1150.00 due in advance. If interest is 16% compounded quarterly and the term of the lease is 4 years, what is the cash value of the lease?

Compute the nominal annual rate of interest compounded monthly at which $1500.00 deposited at the beginning of every three months for ten years will amount to $90 000.00.

At the beginning of every 6 months, $1280.00 is deposited for 8 years at 6.6% compounded monthly. After 8 years interest for the account is to be 9.66% compounded quarterly and the account is to be paid out by equal end-of-quarter quarterly payments over 6 years. What is the size of the quarterly payment?

Mrs. Muirhead paid $27 700.00 into a retirement fund paying interest at 9.32% compounded semi-annually. If she retires in 13.5 years, for how long can Mrs. Muirhead withdraw $5000.00 from the fund every six months? Assume that the first withdrawal is on the date of retirement.

Whitby Honda advertised Honda Pilot for sale at $33 610. The same vehicle could also be leased for 5 years at $379 per month, based on $4310 down payment and a residual value of $10 711. What monthly compounded interest rate was built into the lease?

A rental property provides a monthly income of $1472.00 due at the beginning of every month. What is the cash value of the property if money is worth 7.32% compounded monthly?

Carla plans to invest in a property that after 6.25 years will yield $1457.00 at the end of each month indefinitely. How much should Carla be willing to pay if an alternative investment yields 12.96% compounded monthly?

Cameron is 35 years old and intends to retire at the age of 60. He is planning to contribute $3000 at the beginning of each six-month period to an RRSP. What semi-annually compounded rate of interest must his RRSP earn in order to reach $600 000 after 25 years?

What is the discounted value of deposits of $250.00 made at the beginning of every three months for 10.5 years if money is worth 6% compounded quarterly?

Basim purchased a deferred annuity from an insurance company for $10 971. The money used to purchase the annuity will earn 6% quarterly. The annuity will provide 16 quarterly payments of $1000. If the first payment is to be received on October 1, 2017, when did Basim purchase the deferred annuity?

Fraser deposits $790.00 at the beginning of every three months. He wants to build up his account so that he can withdraw $1550.00 every three months starting three months after the last deposit. If he wants to make the withdrawals for 16 years and interest is 6.64% compounded quarterly, for how long must Fraser make the quarterly deposits?

When Nancy died, she left $20 000 for her 13 year old grandson, Max, to be paid to him as an annual scholarship of $8000 at the beginning of each year, if he ends up in the university. The inheritance was invested in a scholarship fund for 5 years at 9% compounded annually. How long will the scholarship be paid, once Max enters the university?

A debt of $23 900.00 is repaid by making payments of $3617.00 at the beginning of every six months deferred for three years. If interest is 9.6% compounded monthly, for how long will payments have to be made?

The sale of property provides for payments of $10 000.00 due at the beginning of every three months for ten years. If the payments are deferred for five years and interest is 12% compounded monthly, what is the cash value of the property?

What is the principal invested at 6.5% compounded semi-annually from which monthly withdrawals of $840.00 can be made at the beginning of each month for 15.5 years but deferred for 2 years?

Sam got a job at the Brick. He plans to save $500 every month for 3 years to buy a car. The savings account earns 2.25% compounded monthly. If he puts the money in his savings account at the beginning of each month, what will be the present value of the balance in the account at the end of the three-year term?