Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Jamal plans to retire in 17 years. He is saving $2000 every start of the month in a retirement savings account paying him a long-term interest of 9% compounded monthly. What will be the size of his payments at the start of each month from the ordinary simple annuity for 20 years following his retirement?

Triad is considering a medical process that is expected to reduce annual costs by $43 000.00. What is the maximum amount of money that could be invested in the process to be economically feasible if interest is 7.44% compounded quarterly?

Payments of $1000.00 are made into a fund at the beginning of every month for 10 years. If the fund earns interest at 12% compounded monthly, what will the balance in the fund at the end of the term?

The monthly rent payment on computer equipment is $30.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 12% compounded monthly?

Geomax pays $8710.00 at the beginning of each year for using a tract of land. What should the company offer the property owner as a purchase price if interest is 10.18% compounded annually?

A lease agreement valued at $15 000.00 requires payment of $900.00 at the beginning of every quarter for five years. What is the nominal rate of interest charged (compounded quarterly)?

Payments of $500.00 are made at the beginning of each month for four years. The interest rate is 4.5% compounded monthly. If no further deposits are made a) Calculate the accumulated value twelve years after the first deposit. b) Calculate the amount deposited. c) Calculate the interest.

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?

Determine the accumulated value after 15 years of deposits of $500.00 made at the beginning of every 6 months and earning interest at 12% compounded monthly?

What monthly lease payment due in advance should be charged for a tract of land valued at $135 000 if the agreed interest is 8.15% compounded semi-annually?

Jeff is retired and has an investment fund worth $210 000 in an RRSP, which earns 9% compounded semi-annually. He plans to withdraw only $2000 at the beginning of each month starting today. When will the fund become depleted?

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?

What is the discounted value of deposits of $570.00 made at the beginning of every three months for 8.25 years if money is worth 8.4% compounded quarterly?

At the age of 75, Mrs. Walker decided to set up a trust fund for her grandson, which can take care of some of his expenses for the rest of his life. She made an initial contribution of $150 000 to set up the trust fund, which would make the first semi-annual payment of perpetuity to her grandson, 5 years from now. If the funds in trust earn 5% compounded annually, what is the maximum payment the trust can make to Mrs. Walker's grandson in perpetuity?

Mr. Dawson wants to receive payments of $1230.00 at the beginning of every three months for 19 years starting on the date of his retirement. If he retires in 21 years, how much must he deposit in an account at the beginning of every three months if interest on the account is 6.84% compounded quarterly?

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 14th birthday today and the current value of your trust fund is $111 345?

Jawad makes semi-annual contributions of $2000 starting on his 27th birthday. How much will he accumulate in his RRSP by age 60, if RRSP earns 8% compounded annually and no contribution is made on his sixtieth birthday?

The amount of $75 400.00 is invested at 9.65% compounded quarterly for 3 years. After 3 years the balance in the fund is converted into an annuity. If interest on the annuity is 6.75% compounded semi-annually and payments are made at the end of every six months for 8 years, what is the size of the payments?

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?

Rob bought a yacht on a contract requiring monthly payments of $2500 for 5 years beginning on the 6th month after the date of purchase. What was the cash value of the yacht, if interest is 6.9% compounded monthly?