Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Note: The calculations for this question were done using Excel's RATE function. What is the effective rate of interest charged on a lease valued at $17 040.00 if payments of $1180.00 are made at the beginning of each 3 months for four years?

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.

TJ invested a retirement gratuity of $43 000.00 in an income averaging annuity paying 7% compounded monthly. He withdraws the money in equal monthly amounts over five years. If the first withdrawal is made nine months after the deposit, what is the size of each withdrawal?

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 liability will be reported 2 years later?

Jenna intends to contribute $2500 to her RRSP at the beginning of every six months, starting today. The financial adviser has advised Jenna that if she continues her contributions for 20 years, the RRSP would earn 8% compounded semi-annually for the first 7 years and 7% compounded semi-annually, thereafter. What amount will Jenna have in the plan after 20 years?

The sum of $59 760.00 is invested at 9.5% compounded monthly for four years. After the four years, the balance in the fund is converted into an annuity due paying annually $15 240.00. If interest on the annuity is 9.57% compounded annually, what is the term of the annuity?

Knowing that the education costs for her kids would be huge, Roberta puts a lump sum of money from her inheritance in a savings account paying an interest of 4.69% compounded monthly. If ordinary annuity payments of $1500.00 per month are to be paid out of the account at the end of the month for four years starting fifteen years from now, how much did Roberta deposit?

A sum of money is deposited at the end of every month for 9 years at 8.5% compounded monthly. After the last deposit, interest for the account is to be 8.1% compounded quarterly and the account is to be paid out by end-of-quarter quarterly payments of $1800.00 over 7 years. What is the size of the monthly deposit?

A property was purchased for quarterly payments of $1070.00 for 9 years. If the first payment was made on the date of purchase and interest is 5.57% compounded annually, what was the purchase price of the property?

Judy paid for a living room suite over time, signing an installment contract that requires semi-annual payments of $2560.00 for 8.5 years. The first payment is made on the signing date and interest is 14.5% compounded semi-annually. What was the cash price?

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?

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?

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?

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?

Note: The calculations for this question were done using Excel's RATE function. What is the nominal annual rate of interest charged quarterly on a lease valued at $2340.00 if payments of $240.00 are made at the beginning of every three months for 3.25 years?

A retirement gratuity of $123 900.00 is invested in annuity deferred for 10 years. The annuity provides payments of $9600.00 due at the beginning of every six months. If interest is 7.41% compounded annually, for how long will annuity payments be made?

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 present value of the balance in the account at the end of the three-year term?

Starting in 5 years you want to be able to withdraw $6220 every six months for 7.5 years. You want to deposit a single amount immediately and then let it grow at a rate of 4.88% compounded quarterly. How much do you have deposit?

Billy Bean contributes $415.00 at the beginning of each month into RRSP paying interest at 6.25% compounded semi-annually. What will be the accumulated balance in the RRSP at the end of 14.75 years?

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?