Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

The sale of property provides for payments of $10000.00 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?

Jessica bought a bedroom suite on credit, signing an installment contract with a finance company that requires monthly payments of $100.00 for 5 years. The first payment is made on the date of signing and interest is 24% 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?

Quarterly deposits of $2000.00 were made at the beginning of every 3 months for 10 years. If the interest is 6% compounded monthly, what amount can be withdrawn 7 years after the last deposit?

A trust fund will start to pay you $15200 per year at the beginning of each year once you turn 18. The prevailing interest rate is 8.79% compounded annually. For how long can you receive payments if you are celebrating your 14th birthday today and the current value of your trust fund is $111345?

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?

Flin Flon Aqua Club bought swimming equipment on a contract requiring monthly payments of $815.50 for 4 years beginning 11 months after the date of purchase. What was the cash value of the equipment if interest is 7.8% compounded monthly?

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?

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?

Note: The calculations for this question were done using Excel's RATE function. At what nominal rate of interest compounded semi-annually will $2200.00 deposited at the beginning of every six months accumulate to $68 000.00 in 11 years?

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?

What is the accumulated value after 14 years of monthly deposits of $415.00 earning interest at 5.8% compounded semi-annually if the deposits are made a) at the end of each month? b) at the beginning of each month?

A lease requires semi-annual payments of $6100.00 for 7.5 years. If the first payment is due in 3 years and interest is 9.72% compounded monthly, what is the cash value of the lease?

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?

A lease valued at $47 600.00 requires payments of $4500.00 every three months. If the first payment is due 2 years after the lease was signed and interest is 6.88% compounded quarterly, what is the term of the lease?

Calculate the amount of money that needs to be invested today at 4.8% compounded semi-annually to provide monthly payments of $500.00 in perpetuity starting: a) one month from today b) one year from today

Amy contributed $1 011.00 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?

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?

The sale of property provides for payments of $4500.00 due at the beginning of every three months for five years. If the payments are deferred for two years and interest is 6% compounded monthly, what is the cash value of the property?

Determine the future value and the present value of monthly payments of $200.00 each for five years at 12% compounded monthly if a) the payments form an annuity due; b) the payments form an ordinary annuity.

Karen Peters bought their neighbor's farm for $450 000.00 down and payments of $67100.00 at the end of every six months for 7 years. What is the purchase price of the farm if the semi-annual payments are deferred for four years and interest is 5.5% compounded semi-annually?