Exam 13: Annuities Due, Deferred Annuities, and Perpetuities

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?

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?

Mike acquired his sister's share of their business by agreeing to make payments of $4711.00 at the end of each year for 8 years. If the payments are deferred for three years and money is worth 5.96% compounded quarterly, what is the cash value of the sister's share of the business?

The monthly rent payment on photo copier equipment is $671.00 payable in advance. What yearly payment in advance would satisfy the lease if interest is 6.84% compounded monthly?

A contract valued at $81 500.00 requires payment of $3350.00 at the beginning of every six months. If interest is 6.5% compounded semi-annually, what is the term of the contract?

Ellora wants to accumulate $150 000.00 in an RRSP by making annual contributions of $5000.00 at the beginning of each year. If interest is 5.5% compounded quarterly, calculate how long she has to make contributions.

Sandra intends to retire in 15 years and would like to receive $3000.00 every six months for 19 years starting on the date of her retirement. How much must Sandra deposit in an account today if interest is 8% compounded semi-annually?

Aaron Perry bought an income property for $41 321.00 three years ago. He has held the property for the three years without renting it. If he rents the property now, what should be the size of the monthly payment due in advance be if money is worth 6.24% compounded monthly?

Bow Valley Credit Union entered a lease contract valued at $3100.00. The contract provides for payments at the beginning of each month for three years. If interest is 8.8% compounded quarterly, what is the size of the monthly payment?

Calculate the present value of payments of $100.00 made at the beginning of each quarter for ten years if the interest is 6% compounded quarterly.

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?

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?

Determine the accumulated value after 14.5 years of deposits of $172.00 made at the beginning of every 6 months and earning interest at 4.45% compounded monthly?

Sheila intends to retire in 14 years and would like to receive $2472.00 every six months for 9 years starting on the date of her retirement. How much must Sheila deposit in an account today if interest is 6.65% compounded semi-annually?

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?

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?

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.

Note: The calculations for this question were done using Excel's RATE function. What is the nominal annual rate of interest charged quarterly on a lease valued at $2340.00 if payments of $240.00 are made at the beginning of every three months for 3.25 years?

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?

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?