Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Mrs. Martin contributes $1830.00 at the beginning of every three months to an RRSP. Interest on the account is 7.44% compounded quarterly. a) What will the balance in the account be after 6 years? b) How much of the balance will be interest? c) If Mrs. Martin converts the balance after 6 years into an RRIF paying 5.41% compounded quarterly and makes equal quarterly withdrawals for 11 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal? d) What is the combined interest earned by the RRSP and the RRIF?

If you save $150.00 at the beginning of each quarter for 20 years, for how long can you withdraw $800.00 at the beginning of each quarter, starting 20 years from now, and assuming that interest is 9% compounded quarterly?

What monthly lease payment due in advance should be charged for a house valued at $835 000 if the agreed interest is 4.4% compounded semi-annually?

Sean Paul makes deposits of $500.00 at the beginning of every three months. Interest earned by the deposits is 8% compounded quarterly. a) What will the balance in Sean's account be after ten years? b) How much of the balance will Sean have contributed? c) How much of the balance is interest?

Sundeep wants to withdraw $1000.00 at the beginning of each quarter for twelve years. If the withdrawals are deferred to begin ten years from now and interest is 4.5% compounded monthly calculate the amount that must be invested today to be able to make the withdrawals.

How much does a depositor have to save at the beginning of every 6 months for twenty years to accumulate $1 000 000.00 if interest is 6.00% compounded semi-annually?

You bought a camper priced at $15 660.00 on February 1. You agreed to make monthly payments of $575.00 beginning December 1 of the same year. For how long will you have to make these payments if interest is 8.5% compounded monthly?

Olivia plans to have $1 000 000 in her RRSP at her retirement at the age of 60. How long will it take her to accumulate $1 000 000 in an RRSP if the first quarterly contribution of $2000 is made today and RRSP is expected to earn 8% compounded quarterly?

A sum of money is deposited at the beginning of each year for 3 years at 12% compounded annually. After the last deposit interest for the account is to be 8.24% compounded quarterly and the account is to be paid out by payments of $370.00, made at the beginning of each quarter for nine years. What is the size of the annual deposit?

Payments on a six-year lease valued at $12 975.00 are to be made at the beginning of each month during the last 3 years of the lease. If interest is 9% compounded monthly, what is the size of the monthly payments?

Calculate the amount of money that needs to be invested today at 7% compounded semi-annually to provide monthly payments of $2000.00 in perpetuity starting: a) one month from today b) one year from today

Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the start of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded quarterly.

What sum of money must be deposited in a trust fund to provide a scholarship of $630.00 payable at the end of each month if interest is 7.8% compounded monthly?

Determine the future value and the present value of monthly payments of $173.00 each for six years at 6.48% compounded monthly if a) the payments form an annuity due; b) the payments form an ordinary annuity.

Gibran bought a boat valued at $110 194.00 on the installment plan. He made equal semi-annual payments for 6 years. If the first payment is due on the date of purchase and interest is 7.5% compounded semi-annually, what is the size of the semi-annual payments?

Vicki paid for a kitchen set over time, signing an installment contract that requires semi-annual payments of $500.00 for 5 years. The first payment is made on the signing date and interest is 18% compounded semi-annually. What was the cash price?

$6420.00 was invested at a fixed rate of 6.5% compounded semi-annually for 5 years. After 5 years, the fund was converted into an ordinary annuity paying $550.00 per month. If interest on the annuity was 6% compounded monthly, what was the term of the annuity?

Your child is currently six years old. When he turns 19 you want him to be able to withdraw $14700 per year in order to either travel or go to school for four years. If you are able to earn 6.62% compounded semi-annually for the entire time period, what is the single amount of the deposit three years from now that will ensure that your child is able to do this?

Starting three months after her grandchild Crystal's birth, Mrs. Robinson made deposits of $63.25 into a trust fund every three months until Crystal was 19 years old. The trust fund provides for equal withdrawals at the end of each quarter for 5 years beginning three months after the last deposit. If interest is 8.24% compounded quarterly, how much will Crystal receive every three months?

Oakville Aqua Club bought swimming equipment on a contract requiring monthly payments of $1000 for 5 years beginning 6 months after the date of purchase. What was the cash value of the equipment if interest is 12% compounded monthly?