Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

What is the principal invested at 8% compounded semi-annually from which monthly withdrawals of $1000.00 can be made at the beginning of each month for 10 years but deferred for 3 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 balance in the account at the end of the three-year term?

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?

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?

Equal sums of money are withdrawn monthly from a fund of $33 000.00 for 15.25 years. If interest is 9% compounded monthly, what is the size of each withdrawal if the withdrawal is made at the beginning of each month?

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?

Ford Oshawa sells Ford Fusion special edition for a price of $27 900. During a month long promotion, the manufacturer offers an interest rate of 1.8% compounded monthly on a 3-year lease. If the residual value is $14 500, what will be the lease payment at the start of each month with a $2500 down payment?

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?

The monthly rent payment on photo copier equipment is $671.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 6.84% compounded monthly?

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?

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?

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 semi-annually. What is the purchase price of the property?

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 semi-annually and no contribution is made on his sixtieth birthday?

What semi-annual payment must be made into a fund at the beginning of every six months to accumulate to $4800.00 in ten years at 7% compounded semi-annually?

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?

Sheila intends to retire in 14 years and would like to receive $2472.00 every six months for 9 years starting on the date of her retirement. How much must Sheila deposit in an account today if interest is 6.65% compounded semi-annually?

Aaron Perry bought an income property for $41 321.00 three years ago. He has held the property for the three years without renting it. If he rents the property now, what should be the size of the monthly payment due in advance be if money is worth 6.24% compounded monthly?

Carla Craig invested a retirement gratuity of $17 570.00 in an RRSP paying 6.5% compounded semi-annually for 11.5 years. At the end of 11.5 years, she rolled the RRSP balance over into an RRIF paying $1500.00 at the beginning of each month starting with the date of rollover. If interest on the RRIF is 9.5% compounded monthly, for how long will Carla receive monthly payments?

An investment in a lease offers returns of $4000 per month due at the beginning of each month for 5 years. What investment is justified if the returns are deferred for three years and the interest required is 12% compounded monthly?

Babar wants to withdraw $27 000.00 at the beginning of each quarter for twelve years. If the withdrawals are deferred to begin ten years from now and interest is 5.6% compounded monthly calculate the amount that must be invested today to be able to make the withdrawals.