Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

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?

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.

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?

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?

You start to save for a major purchase. You can invest $329 every three months starting today for 5 years and 9 months. You are able to earn 5.87% compounded semi-annually. What is the amount of interest that you earn during the entire term?

The local high school soccer club need to borrow to finance a new soccer field. Repayment of the loan involves payments of $10 000.00 at the end of every three months for eight years. No payments are to be made during the development period of five years. Interest is 8% compounded quarterly. a)How much did the Achievers borrow? b)What amount will be repaid? c)How much of that amount will be interest?

What sum of money must be deposited in a trust fund to provide a scholarship of $1520.00, payable at the beginning of each 3 months, if interest is 6.72% compounded quarterly?

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?

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?

Asif received a bonus of $10 000, which he immediately invested in a fund earning 9.25% compounded semi-annually through his Tax Free Savings Account. Five years later, Asif plans to make the first semi-annual withdrawal of $1000. After how many withdrawals, the fund will be completely depleted?

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?

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?

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?

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.

What monthly lease payment due in advance should be charged for a house valued at $835 000 if the agreed interest is 4.4% compounded semi-annually?

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 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?

A contract valued at 60 000.00 requires payments of $3000.00 at the beginning of each quarter. If interest is 6% compounded quarterly, calculate the term of the contract.

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?

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?