Exam 13: Annuities Due, deferred Annuities, and Perpetuities

A fund to provide an annual scholarship of $5700.00 is to be set up.If the first payment is due in three years and interest is 6.4% compounded quarterly,what sum of money must be deposited in the scholarship fund today?

The Saskatchewan Junior Achievers need to borrow to finance a project.Repayment of the loan involves payments of $8711.00 at the end of every three months for six years.No payments are to be made during the development period of three years.Interest is 9.24% compounded quarterly. a)How much did the Achievers borrow? b)What amount will be repaid? c)How much of that amount will be interest?

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is $700 million,and it will earn interest at 7% compounded annually.Starting 10 years from now,$100 million will be withdrawn from the fund at the beginning of every year for 30 years.What is the annually compounded interest rate for the fund during the final 30 years?

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?

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were made at the beginning of every 3 months for 10 years.If the interest is 6% compounded monthly,what amount can be withdrawn 7 years after the last deposit?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 sum of $15 700.00 is invested at 6.48% compounded semi-annually for eight years.After the eight years,the balance in the fund is converted into an annuity paying equal payments at the end of every 6 months for 5.5 years.If interest on the annuity is 7.95% compounded monthly,what is the size of the equal payments?

Anne-Marie received $445 000.00 from her mother's estate.She wants to set aside part of her inheritance for her retirement 12 years from now.At that time she would like to receive a pension supplement of $2600.00 at the end of each month for 15 years.If the first payment is due one month after her retirement and interest is 3.6% compounded monthly,how much must Anne-Marie set aside?

A trust fund will start to pay you $15 200 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 14^th birthday today and the current value of your trust fund is $111 345?

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?

Kelly is saving $1600.00 at the beginning of each month.How soon can he retire if he wants to have a retirement fund of $345 000.00 and interest is 11.04% 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?

A vacation property was bought by making semi-annual payments of $7500.00 for seven years.If the first payment is due on the date of purchase and interest is 6% p.a.compounded quarterly,calculate the purchase price of the property.

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?

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?

Heavy Mechanical Complex (HMC)acquired a giant lathe machine under a capital lease agreement.HMC pays the lessor $2400 at the beginning of every 3 months for 5 years.If HMC can obtain 5-year financing at 10% compounding quarterly,what long-term lease liability will HMC initially record?

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?

Linda contributes $3000.00 at the beginning of every six months into an RRSP paying interest at 6% compounded semi-annually. a)How much will her RRSP deposits amount to in 15 years? b)How much of the amount will be interest?

Beverley intends to retire in 7.25 years and would like to receive $2700.00 every month for 12.25 years starting on the date of her retirement.How much must she deposit in an account today if interest is 11.36% compounded annually?

Note: The calculations for this question were done using Excel's RATE function. An insurance policy provides for a lump sum benefit of $450 000.00 fifteen years from now.Alternatively,payments of $25700.00 may be received at the beginning of each of the next fifteen years.What is the effective rate of interest if interest is 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?