Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Siri plans to retire when her simple annuity savings account has enough money to receive $10 000.00 per month for twenty years starting at the start of the first month after her retirement. She starts saving $4420 per month. Calculate when should Siri retire from today if her savings account pays 4.9% compounded monthly.

Sagheer is setting up a fund to help his grandson's university education. He wants his grandson to be able to withdraw $3000 every 3 months for 3 years after he starts university. His first withdrawal will be 5 years from now. If the fund can earn 7.2% compounded quarterly, what single amount contributed today will provide for the withdrawal?

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?

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?

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?

Gibran bought a boat valued at $110 194.00 on the installment plan. He made equal semi-annual payments for 6 years. If the first payment is due on the date of purchase and interest is 7.5% compounded semi-annually, what is the size of the semi-annual payments?

Beverley intends to retire in 7.25 years and would like to receive $2700.00 every month for 12.25 years starting on the date of her retirement. How much must she deposit in an account today if interest is 11.36% compounded annually?

Calculate the amount of money that needs to be invested today at 7% compounded semi-annually to provide monthly payments of $2000.00 in perpetuity starting: a)one month from today b)one year from today

Siri plans to retire in 18 years and would like to receive $10 000.00 per month for twenty years starting at the end of the first month after her retirement. Calculate the amount he must invest now if interest is 4.9% compounded quarterly.

Sean Paul makes deposits of $500.00 at the beginning of every three months. Interest earned by the deposits is 8% compounded quarterly. a)What will the balance in Sean's account be after ten years? b)How much of the balance will Sean have contributed? c)How much of the balance is interest?

Payments on a six-year lease value of a car at $27 175.00 are to be made at the beginning of each month during the last 3 years of the lease. If interest is 7.25% compounded monthly, what is the size of the monthly payments?

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?

Starting three months after her grandchild Crystal's birth, Mrs. Robinson made deposits of $63.25 into a trust fund every three months until Crystal was 19 years old. The trust fund provides for equal withdrawals at the end of each quarter for 5 years beginning three months after the last deposit. If interest is 8.24% compounded quarterly, how much will Crystal receive every three months?

How many months will it take to accumulate $17 897.20 at 5.87% compounded semi-annually, if $1140.00 is deposited in an account at the beginning of every 6 months?

Rousan contributed $1900.00 at the beginning of every month to an RRSP. Interest on the account is 4.95% compounded monthly. If she converted the balance after 13 years into an RRIF paying 7.1% compounded quarterly and makes equal quarterly withdrawals for 20 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal?

What sum of money must be deposited in a savings scholarship account to provide a scholarship of $3320.00, payable at the beginning of each 3 months, if interest is 3.59% compounded quarterly?

OPG has set up a fund to help pay the expenses for the monitoring of Pickering nuclear power plant once it is in safe storage. The balance in the fund today is $700 million, and it will earn interest at 7% compounded annually. Starting 10 years from now, $100 million will be withdrawn from the fund at the beginning of every year for 30 years. What is the annually compounded interest rate for the fund during the final 30 years?

Flin Flon Aqua Club bought swimming equipment on a contract requiring monthly payments of $815.50 for 4 years beginning 11 months after the date of purchase. What was the cash value of the equipment if interest is 7.8% compounded monthly?

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?

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?