Exam 13: Annuities Due, deferred Annuities, and Perpetuities

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.

Erica intends to retire in 37.5 years and would like to receive $6600.00 every 6 months for 14 years,starting on the date of her retirement.How much must she deposit in an account today if interest is 6.25% compounded semi-annually?

A sum of money is deposited at the beginning of each year for 3 years at 12% compounded annually.After the last deposit interest for the account is to be 8.24% compounded quarterly and the account is to be paid out by payments of $370.00,made at the beginning of each quarter for nine years.What is the size of the annual deposit?

Sam received a lump sum of $135 000 as an inheritance from his great grandmother.He plans to invest them for 20 years in a long-term investment fund with an expected rate of return of 9% compounded monthly.After 20 years,what payment can he withdraw at the beginning of each month for 10 years?

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?

Li buys a $100 000 life insurance policy,which requires an annual premium of $420 or a monthly premium of $37.In either case,the premium is payable at the beginning of the period of coverage.What is the effective rate of interest Li pays,if he chooses monthly payment plan?

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)?

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?

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?

After retirement,Andy plans to buy bonds in a perpetual fund.What amount must Andy place in a perpetual fund today,if it earns 4.8% compounded semi-annually and the first monthly payment of $500 in perpetuity will be made one year from today?

Mr.Caldwell received a retirement gratuity of $48 700.00,which he deposited in an RRSP.He intends to leave the money for 6 years,then transfer the balance into an RRIF and make equal withdrawals at the end of every six months for 25 years.If interest is 8.5% compounded semi-annually,what will be the size of each withdrawal?

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?

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?

Mark contributed $270.00 at the end of every 3 months for 5.75 years into an RRSP earning 12.6% interest compounded quarterly.Four years after the last contribution he converted the RRSP into a RRIF that is to pay him quarterly payments for 29.5 years.If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 9.5% compounded quarterly,how much will Mark receive every 3 months?

The sale of property provides for payments of $10 000.00 due at the beginning of every three months for ten years.If the payments are deferred for five years and interest is 12% compounded monthly,what is the cash value of the property?

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?

Amy contributed $1011.00 at the end of every six months for 21.5 years into an RRSP earning interest at 6.65% compounded semi-annually.Seven years after the last contribution,Amy converted the RRSP into an RRIF that is to pay her equal quarterly amounts for 17.25 years.If the first payment is due three months after the conversion into the RRIF and interest on the RRIF is 7.66% compounded quarterly,how much will Amy receive every three months?

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?

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?

A man received a separation payment of $98 000.00 at age 56.He invested that sum of money at 8.5% compounded semi-annually until he was 65.At that time he converted the existing balance into an ordinary annuity paying $6150.00 every 6 months,with interest at 5% compounded semi-annually.How many payments will be made?