Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Gary and Sandra Duncan bought a property by making semi-annual payments of $4210.00 for 8.5 years. If the first payment is due on the date of purchase and interest is 8.53% compounded quarterly, what is the purchase price of the property?

If you want to be able to set up a scholarship fund that will last forever and you feel that you can earn 4.8% compounded annually. How much money do you have to deposit today in order to be able to provide 6 scholarships of $3000 each?

The local high school soccer club need to borrow to finance a new soccer field. Repayment of the loan involves payments of $10000.00 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?

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.

Payments of $845.00 are made into a fund at the beginning of every month for 5.25 years. If the fund earns interest at 8.4% compounded monthly, what will the balance in the fund be after 5.25 years?

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?

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?

A sum of $15700.00 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?

Paul intends to retire in 15 years and would like to receive $8000.00 every 6 months for 20 years, starting on the date of his retirement. How much must he deposit in an account today if interest is 5% compounded semi-annually?

Roxanne contributes $167.00 at the beginning of every six months into an RRSP paying interest at 8.9% compounded semi-annually. a) How much will her RRSP deposits amount to in 31.5 years? b) How much of the amount will be interest?

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?

How much does a depositor have to save at the beginning of every 6 months for eleven years to accumulate $17 448.00 if interest is 6.25% compounded semi-annually?

A property was purchased for quarterly payments of $3000.00 for 10 years. If the first payment was made on the date of purchase and interest is 6% compounded annually, what was the purchase price of the property?

How much extra interest do you gain by starting today rather than waiting one year if you want to deposit $1710 per year for 28 years? You are able to earn 7.07% compounded annually.

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?

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?

$6420.00 was invested at a fixed rate of 6.5% compounded semi-annually for 5 years. After 5 years, the fund was converted into an ordinary annuity paying $550.00 per month. If interest on the annuity was 6% compounded monthly, what was the term of the annuity?

Robert Bernard deposited $1000.00 in a trust account on the day of his son's birth and every three months thereafter. If interest paid is 8% compounded quarterly, what will the balance in the trust account be before the deposit is made on the son's twenty-first birthday?

Joshua deposited $3560.00 at the beginning of every 6 months for 11 years into a fund paying 3.5% compounded semi-annually. Fourteen years after the first deposit he converted the then existing balance into an annuity due paying him equal annual payments for 22 years. If interest for the annuity due is 5% compounded annually, what is the size of the annual payment?