Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

Starting in 5 years and 6 months you want to be able to withdraw $950 every three months for 3 years and 3 months. You want to deposit a single amount immediately and then let it grow at a rate of 7.24% compounded quarterly. How much interest did you earn during the entire period of time?

If you save $150.00 at the beginning of each quarter for 20 years, for how long can you withdraw $800.00 at the beginning of each quarter, starting 20 years from now, and assuming that interest is 9% compounded quarterly?

You bought a camper priced at $15 660.00 on February 1. You agreed to make monthly payments of $575.00 beginning December 1 of the same year. For how long will you have to make these payments if interest is 8.5% compounded monthly?

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?

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 monthly.

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?

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)?

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?

Tom started his career with Oracle with an intention to retire in 25 years. When he retired, he started receiving $66 000.00 every 6 months for 15 years, starting on the date of his retirement. How much did Tom deposit deposit in an account at the start of his career, if interest is 9.25% compounded semi-annually?

The amount of $75 400.00 is invested at 9.65% compounded quarterly for 3 years. After 3 years the balance in the fund is converted into an annuity. If interest on the annuity is 6.75% compounded semi-annually and payments are made at the end of every six months for 8 years, what is the size of the payments?

Mrs. Martin contributes $1830.00 at the beginning of every three months to an RRSP. Interest on the account is 7.44% compounded quarterly. a)What will the balance in the account be after 6 years? b)How much of the balance will be interest? c)If Mrs. Martin converts the balance after 6 years into an RRIF paying 5.41% compounded quarterly and makes equal quarterly withdrawals for 11 years starting three months after the conversion into the RRIF, what is the size of the quarterly withdrawal? d)What is the combined interest earned by the RRSP and the RRIF?

Quarterly deposits of $650.00 were made at the beginning of every 3 months for 11.25 years. If the interest is 4.92% compounded monthly, what amount can be withdrawn 6 years after the last deposit?

Mrs. Muirhead paid $27 700.00 into a retirement fund paying interest at 9.32% compounded semi-annually. If she retires in 13.5 years, for how long can Mrs. Muirhead withdraw $5000.00 from the fund every six months? Assume that the first withdrawal is on the date of retirement.

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?

What is the accumulated value after 15 years of monthly deposits of $500.00 earning interest at 8% compounded semi-annually if the deposits are made a)at the end of each month? b)at the beginning of each month?

How much does a depositor have to save at the beginning of every three months for 15 years to accumulate $200 000.00 if interest is 4% compounded quarterly?

Carla plans to invest in a property that after 6.25 years will yield $1457.00 at the end of each month indefinitely. How much should Carla be willing to pay if an alternative investment yields 12.96% compounded monthly?

Keith bought a lakeside cottage for 30% down and monthly mortgage payments of $1224.51 at the beginning of each month for 20 years. Interest is 4.4% compounded monthly. What is the purchase price of the property?

Linda contributes $3000.00 at the beginning of every six months into an RRSP paying interest at 6% compounded semi-annually. a)How much will her RRSP deposits amount to in 15 years? b)How much of the amount will be interest?

Robert Downey deposited $610.00 in a trust account on the day of his son's birth and every three months thereafter. If interest paid is 7.2% compounded quarterly, what will the balance in the trust account be before the deposit is made on the son's twenty-first birthday?